If you're behind a web filter, please make sure that the domain *.kastatic.org is unblocked.

Watch the entire video

Back

Discussion and questions for this video
Can both a and b equal the same for example x^2+20x+100 can both a and b equal 10?
Yes the number does not have to be different.
What's a coeffcient?
A coefficient is a term in mathematics which is basically the number that we used in this expression to multiply a variable. so X has a coefficient of 1, and 2X has a coefficient of 2, and so on.
watch closely in the video at 01:35, Sal (the teacher) is referring to the middle coefficient (which is of the variable " B ") as 10, meaning its 10 times B or just 10B.

further information > http://en.wikipedia.org/wiki/Coefficient
1 Comment
how come the constant term is the product of a and b?
1 Comment
The constant term is a*b because when you do F.O.I.L. when you multiply (x+a)(x+b), you have to multiply a and b at the last stage. This will be a constant number because a and b are constant numbers. Neither is attached to a variable.
1 Vote
Comment
Why would you need to factor a quadratic in the first place?
1 Comment
So that we can........
1.) Find the value of a missing variable, such as x.
2.) Cancel out something that is on the numerator and the denominator to simplify rational expressions.
For instance if we have something like....
x²-2x-80/x²+16x+64
(x-10)(x+8)/(x+8)(x+8)→As we can see we can now cancel out an (x+8) here to simplify it to.....
x-10/x+8
There are a lot of videos on factoring by grouping. We have to learn to do it by trial and error. Are there videos for that too? How would you find 8x^2 -14x+3?
1 Comment
Even simpler (so as to avoid the fractions), if the quadratic is in the form:
ax^2 + bx + c
where a is not 1, you can do the following:

Multiply a and c to get a new number (say d). Now, you must find two numbers that add up to b, and multiply to d.
x + y = b
x*y = d = a*c

So in your example above, you would see that d = a*c = 8*3 = 24. Two numbers that add up to b = -14 and multiply to d = 24 are x = -12, and y = -2.

Then you can simply group and factor to get the correct answer.
1 Comment
how will i know what x is in the equation x^2-5x+24?
Comment
You cannot work out what x is in the expression x^2-5x+24. This is because expressions cannot be solved as they do are not equal to anything. E.g they are like statements.

If x^2-5x+24 was equal to a number or another expression then we would be able to work out the value of x.

For example:
x+1 (x could be equal to any number)
BUT
x+1 = 3 (x can only be equal to 2)

I hope that helps
Comment
Are there suppose to be alot of steps to this ?
Comment
i think there are around like seven steps maybe
1 Vote
1 Comment
What would be considered a constant?
Comment
A fixed value.

In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

Example: in "x + 5 = 9", 5 and 9 are constants

If it is not a constant it is called a variable.

-- taken from "math is fun"
Comment
What if the numbers are prime and have no factors?
Comment
All quadratics can be factored, but not all of them can be factored with rational numbers or even real numbers. If a quadratic cannot be factored into rational factors, it is said to be irreducible. However, it is always possible to factor a quadratic, if you allow irrational or complex factors.

Here's how to factor ANY quadratic expression in the form: ax² + bx+c.
Let d = b² - 4ac
(If d is not a positive perfect square, then the quadratic is "irreducible".)
The factors are:
a [x + ¹⁄₂ₐ (b + √d)] [x + ¹⁄₂ₐ (b - √d)]
If it makes for convenient numbers, you may use the distributive property to multiply a into one (but not both) of the factors.
Comment
How do you factor a polynomial when the highest power is greater than ^2?
Comment
Long Division of Polynomials or Synthetic Division.
Comment
Do the numbers have to be whole, or could you end up with an answer like (x+2.5)(x+5.7)?
Comment
Yes, that could certainly happen. The quadratic expression x^2 + 4x + 3.75 factorises into (x + 1.5)(x + 2.5), for example. But (at least at first) you will probably find that the examples you are given factorise into integers.
Comment
At 14:49, can you do (-x-3)(x+8) instead of -1(x-3)(x+8)?
Comment
No. The distributive property is not being properly used.

You are trying to multiply -1 by (x-3). Using the distributive property, you'll get -x+3 as a result. So it should be (-x+3)(x+8).
1 Comment
what if we have:
7x^2-31x-20
How do we do that?
Comment
Neha,
To factor 7x^2-31x-20
First multiply the first and last numbers. 7*20 = 140.
Factor 140 to its primes 7*5*2*2
Now find two numbers that multiply to 140 and subtract to 31
You need a number that is more than 31 so start with
7*5=35 and 2*2 = 4 And we got it first guess 35-4 = 31
We know the x values are
(7x ± ? )(1x ± ?)
You know the 7 need multiplies by the 5 so the second ? is 5
(7x ± ? )(1x ± 5) The other ? must be 4
(7x ± 4 )(1x ± 5)
The 20 is a -20 so one sign must be + and the other must be -
The middle factor is -31 not +31 so the 7*5 must be negative so use -5
(7x ± 4 )(1x - 5) And as we already said the other sign must be +
(7x + 4 )(x - 5)

7x^2-31x-20 factors to (7x + 4)( x - 5)

I hope that helps make it click for you.
What is a degree of a polynomial
Comment
The degree of a polynomial is whatever the exponent is of the variable with the highest powered exponent. For example, a quadratic is a second degree polynomial and cubic is a third degree polynomial.
Comment
I have a question on solving but I can't find a video that deals with the topic (probably because I don't know what this type of problem is called) Could someone point me in the right direction or solve this step by step for me?

Solve for x
x^4-13x^2+36=0
answers given on the sheet are {3, -3, 2, -2}
my first thought was to reduce to x^2-13x+6=0 and solve from there using the quadratic formula but my answers don't match the answers on the handout and I only got two when we are supposed to find four, how do you get four?

Thanks!
1 Vote
Comment
simplify your life and from the very beginning, substitute a different variable in to stand for x^2 the whole time until you've got it solved and are ready for the final answer.
Say, g=x^2. So, just deal with this equation: g^2-13g+36=0.
Factor: Two numbers that multiply to be 36 and add up to be -13 are -9 and -4.
(g-9)(g-4) = 0. Now, set each part equal to zero.
g-9=0 ; g-4=0
so, g=9 ; g=4. NOW, bring back the x^2 instead of g again.
x^2 = 9 ; x^2 = 4
so, x can be -3, 3, -2, or 2.
Comment
Do we use FOIl for this problem?HELP
Comment
Once you have a quadratic formula in (x-a)(x-b) form, you don't need to use FOIL. If you do, you just get the original equation. The answers are a and b.
Comment
What if you get a polynomial with 4 terms? Even 5?
Comment
What I mean is that polynomials with 4 or more distinct terms. Such as:

x^2 + 4x + 2xy + 10y

In which there are no like terms.
1 Vote
Comment
So, what would a real life problem for using this be? How would you use it with other parts of math? Please ask me a question if you are confused about what I mean here! Thanks!
Comment
age problems, research and other things
1 Vote
Will this method always work?
Comment
only if you have a trinomial
1 Vote
Comment
I have no idea how to transform rational functions into graphing form
For exam le -4/4x↑2 +40x+ 10
Do I factor the bottom im so confused I'm not any good at precalculus it frustrates me because people in my class seem to get it I feel horrible and my teacher refuses to help :(
Comment
-4/4x² +40x+ 10
First we simplify by cancelling out the 4's to get: 1/x²
The common denominator is x², so we multiply everything by the factor that would given them that denominator -- it is just the same idea as adding fractions. In this case, one term already has that denominator, the other two need to be multiplied by x² / x² (remember what you did with adding ordinary fractions). This will give you:
-1/x² + (40x)( x²/x²) + 10(x²/x²)
= (-1 + 40x³ + 10x²) / x²
= (40x³ + 10x² - 1) / x²
You cannot simplify this any further. If you could tell me what it is equal to, I could finish solving the problem. Of course, if it is just equal to y or f(x) then that is as simple as it gets.
1 Vote
Comment
Do *un-factorable* polynomials exist?

For example:

x^2+8x+36
Comment
That is a great question. The anwer is actually yes. There are un-factorable (or irreducible) polynomials and the reason why can go very deep into mathematics. It is something that people study is college and beyond. Another simple polynomial that can not be factored is x^2+1. To see why suppose it factored as (x+a)(x+b). Then we would need a+b=0 and ab=1. The first equations tells us that either both 'a' and 'b' are 0 or one and not the other is negative. From there we see that both equations can not be true at the same time (did that make sense?) The same kind of thing is true about your polynomial.

It turns out that you can always factor polynomials with degree greater than 2 into smaller polynomials but there are many degree 2 polynomials that can not be factored. If you want to know more about this you will probably have to learn about roots of equations and then maybe the imaginary numbers like the square root of -1.
1 Comment
Comment
Quadatus is latin for square. Quadratic pertains to a square. If you have a term in an expression or equation that is to the second degree or squared, it is called quadratic.
Comment
i need help with this!
5x^2=15x
ive got it to where its equal to zero but i cant get past that
Comment
5x²=15x
x²=3x
x²-3x = 0
x(x-3)=0
x=0 or
x-3=0
x = 3
Thus, x= 3 or x=0
Comment
Is this the easiest way of factoring?
Comment
The easiest method is the one which works the best for you
1 Vote
Comment
Is this also referred to as " Factoring x^2+bx+c". My book goes over this and calls it so. Why is it called Factoring quadratic Expressions here on KA? I'm confused.
Comment
Comment
Expressions of the form ax^2 + bx + c; where a is not 0.
Comment
What's a coeffcient?
Comment
A coefficient is a constant (like "5") that is multiplied by a variable.
1 Vote
Comment
What's a coeffcient?
Comment
A co-effient is the number before the variable. eg. in -3x, -3 is the co-efficient. The variable is x. Variables are used to represent unknown numbers.
Comment
What Is A Degree?
Comment
A degree is a unit of measurement of angles. It is also equal to 1/360th of the circumference of a circle. º is its symbol.
I hope this helps!
1 Comment
Can you give some factoring examples that have no solution, one solution, and many solutions. And are there any examples that cannot be factored?
1 Vote
Comment
Well, all quadratics can be factored if you allow irrational and complex factors. But, if you mean rational factors, there are plenty that cannot be factored:
2x²+x+15 cannot be factored with real numbers.
No quadratic has "many" factors: Either there are two real, one real, or no real factors. If you have irrational or complex factors, you always have two of them (if there are no irrational or complex numbers in the quadratic expression).
As for having just one factor, it will always be the case that you really have two identical factors. For example, x²+6x+9 factors as (x+3)(x+3) also written as (x+3)².

No quadratic has more than two factors (unless you count factoring out a common factor such as:
2x² + 6x + 4 = 2(x² + 3x + 2) = 2(x+1)(x+2)
Comment
How do you factor t^2 = 5t?
1 Comment
Alright here's how we do it.
t^2 = 5t → This is what we were given.
t^2 − 5t = 0 → I subtracted both sides by 5t
t(t−5) = 0 → Notice that both t^2 and 5t have a common factor of t so we can just factor that out and we're done!

We now also what the value t should be so that the equation will equal 0. Which is t=5
Let's try substituting the value of t here.
t(t−5) = 0 → This is the original equation.
5(5−5) = 0 → I now substituted 5 in place of t in the original equation.
5(0)=0 →This what we'll get
0=0 → And we finally checked that our answer is correct.

Although it it might have been easier (depending to the person) to solve it by dividing both sides by t.
t^2 = 5t → This is what we were given.
(t^2)/t = 5t/t → I'm dividing both sides here by t
t=5 → and there's my answer.
1 Vote
Comment
why do you start factoring out a -1 in the last two equations of this video?
it seems like extra work and you don't explain why you do it, other than "it makes it easier". how does it make it easier?
Comment
3x^2-10x+5=0 cannot be factored, why?
Comment
Sure it can. The easiest way to do it is probably to use the quadratic formula.

1 Vote
Comment
What level of math would this be considered? Algebra 1? Algebra 2? College Algebra? Thanks!
1 Vote
Comment
yea i'm learning this in Algebra 1
Comment
Maybe this isn't the right place to ask, but I have a question I need solved.
How would I factorise (x-1)^2 - (x-5)^2? My teacher says 8(x-3) is wrong. Any ideas?
1 Vote
Comment
(x-1)² - (x-5)²
= x²-2x+1 -x² +10x -25
= (x² -x²) + (10x -2x) + (1 - 25)
= 0 + 8x - 24
= 8x - 24
= 8(x-3)
1 Comment
what are polynomials?
Comment
A group of several terms.
1 Vote
Comment
Comment
factoring quadratic expressions….. JK… I really don't know.
1 Vote
Comment
What are first and second degree terms?
Comment
Examples of first degree terms: 7x, 4, 89z, 23r
Examples of second degree terms: 3x^2, 64y^2 18p^2
Examples of third degree terms: 23x^3, 34^y^2 87o^3
and so on...
1 Vote
Comment
how would you solve questions like x squared + 19x + 17, since 17 is a prime # and the sum of it's only 2 factors add up to 18, what would you do instead?
Comment
You could complete the square to
x^2 + 19x + (19/2)^2 = (19/2)^2 - 17

Either way, you will get two factors with expressions that include the square root of 293.
1 Vote
Comment
ughh i just got confused again whats 3a^2+7a+2 my techer just mixed up my brain:[ im way to new at this
Comment
Try going to math tutoring on tuesdays, wednesday, & thursdays, it helps alittle better .
1 Vote
Comment
What's a coeffcient?
1 Vote
Comment
A coefficient is the number in front of a variable that is intended to be multiplied by that variable. For example:
4x has a coefficient of 4
but,
4 + x has a coefficient of 1
(if nothing is shown, the coefficient is 1)
Comment
How can i relate factoring quadratioc equations to real life ?
1 Vote
Comment
I have a problem that's X^2 + X + 1 in my text book it just says prime.... what does that even mean?
1 Vote
Comment
Prime means that the expression cannot be factored any further because each term in the expression has no GCF.
Comment
In my school, they taught us a technique called "Splitting the middle term" to factor quadratics.
How it goes is, we think of two numbers that add up to the co-efficient of x but also when multiplied those two numbers form the product of the coefficient of x^2 and the constant term.(We ,often, prime factorize the "product" and then go by trial and error to find the "sum").
Then we replace our x term with two other x terms which have the numbers we thought of as respective co-efficients. Then we proceed to reverse engineer the polynomial to make it into the form (x+a)(x+b).

Now, can somebody explain to me why the method Sal is teaching me is so ridiculously similar?

Also, which method is easier? Splitting the Middle Term OR Sal's Factoring Quadratic expressions.
1 Vote
Comment
3:11- can the the number be 5 and 5 instead of 1 and 9
1 Vote
Comment
Sadly, it can't be 5 and 5. Here is why:

x^2 + 10x + 9

You have to find numbers that can add up to 10 and multiply to be 9.
When using 5 and 5, the numbers would add up to 10, but would multiply to be 25.
When using 1 and 9, the numbers add up to 10 and multiply to be 9
1 Vote
Comment
Comment
how do I factor the following question(x^3-x^2+x-1)
1 Vote
Comment
At 00:54, why does Sal use the expression (x+a)(x+b) to solve the problem? Is that a formula?
1 Vote
Comment
No, that's not a formula. That's just your basic form for what your answer should be after factoring. The basic goal is to have a + b equal to the middle x term, and have a x b equal to the last number term.

So, by finding factors of 9: 1, 3, and 9, and then seeing which two add up to 10 ( 1 and 9) you can factor the equation to (x + 9)(x + 1).
Comment
i really do not understand how to factor at all and i have these huge problems i can not do for example -56m^2+117m-55
1 Vote
Comment
Well this is a tough one. If you are really struggling I would suggest working on some easier ones first since the explanation I am about to give uses a lot of problem solving skills that are easier to develop with simpler problems.

We are looking for something of the form (nx+a)(mx+b). When we multiply this out we get nmx^2+nbx+max+ab=nmx^2+(nb+ma)x+ab. We get three equalities from this found by matching the constant terms, the x terms, and the x^2 terms. First mn=-56, next nb+ma=117, last ab=-55. The reason this problem is difficult is that you have to choose what to try and making good choices comes with practice. I would say start with ab=-55 because 55 only has two factors. So we just take a guess that a=55 and b=-1. Then nb+ma=117 means that m is probably small and positive so lets let it be 2. Then we have n(-1)+2(55)=117 so n=-7 but unfortunately 3(-7)=-21 is not equal to -56.

We could try other m's but I don't think it will work so lets switch to a=11 and b=-5. Well m is a factor of -56=-2*2*2*7 so lets try m=8. Then -5n+11(8)=117 means n=-29/5 so not right. m=14 gives n=37/5 so that doesn't work either and we went to high with m. If m=7 then n=-8 which works! We are done. The answer is (-8x+11)(7x-5).

As you saw there was a lot of guessing and trying things. It could have taken a lot longer if I was not aware of what would be good guesses and when to stop following a track. This comes with practice.
Comment
x2-4x= -4 how do you solve? i need help.
1 Vote
1 Comment
Essentially these types of questions are asking for you to solve for x.
How you would do this:
Add 4 to both sides then you would get x^2-4x+4=0 which you can factor to get
1 Vote
Comment
At 14:49, can you simplify the problem -1(x-3)(x+8)? If so, would the answer be (-x+3)(-x-8)? Or would it be (-x+3)(x+8)?
1 Vote
Comment
-1(x-12)(x-6). should you write this like -1((x-12)(x-6)) or is it a rule to multiply the parentheses with each other first?
1 Vote
Comment
Nicholas,
You get the same answer if you do it either way.
(-1(x-12))(x-6) = -1((x-12)(x-6))
This is because of the associative property of multiplication.
The associative property is (a*b)*c = a*(b*c)
Comment
What is th purpose of factoring by grouping? I don't understand how, by what advatnge does it give?
1 Vote
Comment
Factoring is a way to find the value for x in a quadratic. (Try just solving for x the way you would do a linear equation. It doesn't work, does it :P)
There are several ways to solve for x in a quadratic (completing the square, quadratic formula, factoring, etc.) However, for simpler quadratics, factoring tends to be the quickest and easiest for most people.
Hope this helps!
Comment
Okay, my problem is 6r^2+16r-32=0 im at 2(3r^2+8r-16) Now what do I do?
1 Vote
Comment
2(3r²+8r-16)
That much is correct. As for finding the rest, many people just try to guess the factors, but that takes up time and doesn't always work. Here's how to do it systematically, for when you can't easily guess the factors:
To make this easier to follow, I will just factor the part you've not factored yet (in real work, you should carry the 2 along the whole way, but we'll just ignore it for the moment.)
3r²+8r-16
we will split the middle term into two terms, mr + nr such that:
m + n = 8 (this is the coefficient of the middle term)
mn = (3)(-16) = - 48 (this is the product of the coefficients of the a and c terms).
Looking at the pairs of factors of -48, we see which of them add to 8 (and of course, multiply to be -48). I won't go through the whole list of possible factors that you would have to eliminate, but you'd get 12 and -4.

So, we split 8x into 12x - 4x
This gives us:
3r²+8r-16
= 3r² + 12r - 4r -16
We factor the first two and then the second two:
= 3r(r + 4) - 4r -16
= 3r(r + 4) - 4(r+4)
There now is a common factor, so we factor (r+4) out:
= (r + 4)(3r - 4)
2(r + 4)(3r - 4)
Can anyone tell me why it's called a quadratic expression?
1 Vote
Comment
1 Vote
Comment
Okay, so my problem is x^2-12x+32=0... My problem is why does my answer sheet tell me that the answer is 8 and 4. I got -8, -4. which makes more since to me. I understand how 8 and 4 could be right... but checking it.. It doesn't.. Here--- (x+4)(x+8) -->x^2+8x+4x+32= x^2+12x+32.. Not x^2-12x+32.. BUT, if I do -4,-8 then I get---- (x-4)(x-8)---->x^2-8x-4x+32= x^2-12x+32. Which is the original equation.. Help?
1 Vote
Comment
You are confusing the roots with the factors.
x² - 12x+ 32 = 0
(x-4)(x-8) = 0
So the factors, not the roots, are (x-4) and (x-8).
To get to the roots, you find those values of x for which the equation is true. In this case, (x-4)(x-8) = 0 is true whenever either factor equals 0.
Thus the roots (also called solutions) are:
x-4 = 0 OR x-8 = 0
Solving each equation gives us
x = 4 OR x = 8

The distinction between factors and roots might be easier to see in a problem like this: 6x² + x - 35 = 0
This factors to: (2x+5)(3x-7)=0

So, the factors are (2x+5) and (3x-7).

The solutions, or roots, are:
(2x+5)=0
2x = -5
x = -5/2
OR
3x-7 = 0
3x = 7
x = 7/3
So the roots, or solutions, are x=7/3 OR x= -5/2

Hopefully you can see how, though related, the factors and the roots are not the same thing.
Comment
When we swap a number from a side to the other side, we make it a negative number, don't we?
1 Vote
Comment
I get it now. Thank you.
1 Vote
Comment
Even though I watched the whole video, I still don't get it .. this is hard ! Can someone explain this to me more easier ?
Comment
trust me it gets harder can u help me on mine its like up there
Comment
In this video, Sal doesn't seem to go over problems like this: (a number)x = -x^2-(a number). I am having trouble finding a video on these specific kind of problems, anybody know where I can find another one of these videos on khanacademy, or elsewhere?
1 Vote
Comment
How would you factor the equation if there were a number in front of the x^2? ex: 5x^2+10x+9 ??
1 Vote
Comment
what is a polynomial ?
1 Vote
Comment
hey what if you have like 24 and 10x its 6 and 4 or 8 and 3 how do you tell what one to use?
1 Vote
Comment
what is a polynomial?
1 Vote
Comment
Why is it called quadratic if it is raised to the second power. Shouldn't it be called bidratic or something?
1 Vote
Comment
It actually comes from the Latin word "quadratum", which means "square". The reason lies in geometry: x^2 is the surface of a square with sides of length x.
Comment
So are there quadratic expressions that can't be factored? (For example if the constant term is a prime and the first degree coefficient is ≠ the constant term ± 1)
1 Vote
Comment
(x+a)(x+b) can be used to factor all quadratics, correct?
1 Vote
Comment
How do I factor 5/7ab-35b
1 Vote
Comment
This question might be a little stupid but what's a polynomial and binomials????
1 Vote
Comment
idk. its not a stupid question.
1 Vote
Comment
At 15:10, why can't a * b be taken directly as (-1)(-72) ? Is that a wrong method?
1 Vote
Comment
Is it quadratic function only when it can be factored out?
For example if I have
x^2 + 17x + 1
Is it not quadratic function anymore?
1 Vote
Comment
How would you factor 3x^2 −5x−2? The solution is (3x + 1)(x - 2) but I don't understand how? Using the method, factoring -2 I cant figure anything out that satisfies how it equals to 5?
1 Vote
Comment
A Man,
Multiply the outside terms
3x * -2 = -6x
Multiply the inside terms
1 * x = 1x
-6x + 1x = -5x

Does that help?
1 Vote
Comment
I have a question. How do you know if its (x-4)(x+3) or (x-3)(x+4)?
1 Vote
Comment
Even though a*b and b*a are the same answer, -12, look at (a+b). For your first example it is (-4+3)=-1. For your second example (-3+4)=1. Therefore, your first example would be correct for x^2-x-12=0 and your second example would be correct for x^2+x-12=0.
1 Vote
Comment
how do you solve x^2+9x+13=(x+4)(x+5)=m
1 Vote
Comment
You can't. (x + 4)(x + 5) = x^2 + 9x + 20.
1 Vote
1 Comment
How to factor 3x^2-2x?
1 Vote
Comment
how do we solve it when a is greater than 1 or less than -1
1 Vote
Comment
Hey how do we solve this find A and B
(Ax+B)(3x^2-2x-1) = 6x^3 - 7x^2 + 1

And which videos do I find related to this ....
1 Vote
Comment
Thanks a lot :)
1 Vote
Comment
At 16:04 for the expression -(x^2-18x+72), couldn't Sal take out a common factor of -9 to change the expression to -9(x^2-2x+8) ?
1 Vote
Comment
There is no 9 in the x^2 term. He would have to change it to -9(1/9 x^2 - 2x + 8) if he did that.
1 Vote
Comment
1 Vote
Comment
So when we solve this equation, we break it down into two seperate pieces. So we know for certain one of the pieces will be (5x+?) and the second piece will be (x+?). So then we find the possible numbers that can go into these pieces. One number is +/-1 and another number is +/-2 (we get when finding the factors of -2. We then plug these numbers into (5x+?)*(x+?) until we get (5x^2-3x-2. We eventually find that (5x+2)(x-1)=0. Then we solve for x in 5x+2=0 and x-1=0. We get x= -2/5 and 1. Hope this helped. :)
1 Vote
Comment
So, to clarify:

Determining 2 Factors of the *Constant Term* and getting them in the [x+F1][x+F2] form is nothing but a shortcut to the Factoring by Grouping way of doing things, am I correct?

Thanks!
1 Vote
Comment
How do you figure out a question that has the answer but you have to figure out x's value?
For example: x^2 - 3x -18 = 0
Is there an easier or faster way to figure out what x equals besides guess and check?
1 Vote
Comment
To factor the polynomial more easily look at the videos on completing the square or the quadratic formula.
1 Vote
Comment
what if you have a number in front of the variable squared???
Comment
in 0:59, is the topic his is talking about distributive property, just with variables?
1 Vote
Comment
I have a quadratic I can't seem to figure out Help!
y= -xSquared + 2x + 4 Cant seem to get it with the example above? what am I doing wrong?
1 Vote
Comment
Well, the coefficient of x squared is -1, not 1, so the method is completely different. You should watch another video, explaining how to do it. Basically, you have to find factors of both, -1x and 4, and work it from there. The problem you presented is a little hard, and I can't find the answer instantaneously, so I suggest watching another video. Ask if you need more help, ok? ;)
1 Vote
Comment
What if the first number is not a 1x squared but say 6x squared
1 Vote
Comment
You would try different ways of getting for example 6x^2 which would be 3 and 2. but it could also be 6 and 1 depending on the rest of the probelm. Just makde sure you check your inner and outer to see if it works!! Hope that helps!
1 Vote
Comment
Why does a+b =negative instead of positive
1 Vote
Comment
Carl,
a+b equals a negative number only when the coefficient on the x value is negative.
a*b = negative when the coefficient on the constant value (the one without the x) is negative.

I hope that helps
1 Vote
Comment
Factor the trinomial x^2+5x+47
1 Vote
Comment
where did you get a and b from?
1 Vote
Comment
i know factoring Quadratic Expressions like a*b and a+b but how do i Know it easier
1 Vote
Comment
If you have 8x/\2+etc., how would you put that in (x+a)(x+b)?
1 Vote
Comment
does this method work if the variable is not a square?
1 Vote
Comment
For factoring a quadratic expression, do the signs always have to be addition signs? If not, is there another formula to it?
1 Vote
Comment
Where did he get the polynomial from
1 Vote
Comment
How do you factor an equation such as 2x^2+8x+8? Or anything with a higher or lower coefficient than 1 for x^2?
1 Vote
Comment
(2x + 4)(x+2)
You factor it the exact same as if there wasn't a coefficient >1, it's just a little trickier.
1 Vote
Comment
Is it always x squared, or can it be different. For example, 2x squared, 3x squared, ect.
1 Vote
Comment
yes it can have anything as its coefficent
1 Vote
Comment
Thanks for your answer James Pearson! I just had one more question in this case -- why is (-x)(x) not -x², and why is (-x)(-x) = -x², as I thought if you multiplied a negative by a negative it becomes positive? If you have (-x+3)(-x-8), wouldn't it end up being -x multiplied by -8, which would be 8x, added to -x multiplied by 3, which would be -3x, giving us +5x? However, in the original equation it is a negative -5x, which I don't understand.
1 Vote
Comment
What about if it is 7m^4-54m^2-16
1 Vote
Comment
Well, 7m^4-54m^2-16 is able to be simplified.
(m^2-8)(7m^2+2)
If you solve this using the foil method, it is 7m^4+2m^2-56m^2-16, then simplify
1 Vote
Comment
what do you mean by factoring out the negative one at 13;00 ?
1 Vote
Comment
The idea is that he doesn't want the x squared to be a negative, since that would make the entire equation more difficult, so the simplest way to solve it and make it like the previous equations he'd been solving for us, was to make the negative x squared into a positive. He did that by factoring out the -1, making the first term positive and making it exactly like the other ones that you had seen. Hope this helped!
1 Vote
Comment
what do you do if you have an expression like this-
14x^2-15x+4
1 Vote
Comment
not allowed to use it... :(
1 Vote
Comment
what is 4+4 (4a-)
1 Vote
1 Comment
it equals 4+16a
1 Vote
Comment
What if the expressions looks like this:--- 9x^2-1, 4x^2-36 and 9x^2-4, how do I factor this quadratic equation?
1 Vote
Comment
Im just curious when would this ever be useful in real life? in a physics or engineering job?
1 Vote
Comment
Report a mistake in the video
Example:

At 2:33, Sal said "single bonds" but meant "covalent bonds."

Discuss the site

Flag inappropriate posts

Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.

abuse
• disrespectful or offensive
• low quality
• not about the video topic
• a homework question