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2x^2+4x-240

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4 Answers

2x2+4x-240=2(x2 + 2x - 120)

(x2 + 2x - 120)=(x2 + 2x +1-1-120)

Do you wonder where those 1's come from? Here is the trick. In the expression x2+ 2x - 120, we particularly look at the second term, which is 2x. When we divide the 2 in front of the x by 2, we obtain 1. 

The 1 in this case is the number that will help us in the factorization. We create a 1 in the expression, and at the same time we create another number -1 to cancel the 1 that we created. Look at the following steps carefully to see how the 1 and the -1 are rearranged.

(x2 + 2x+1) - (1+120)=(x2 + 2x+1)-121=(x+1)2-112

If you know that a2-b2=(a+b)(a-b),  we do the following substitutions : a=(x+1) and b=11

(x+1)2-112=(x+1+11)(x+1-11)=(x+12)(x-10)

Finally 2x2+4x-240=2(x+12)(x-10)

When I look at something I am going to factor, I try to see if I can make things easier for myself. What seems to be the hardest part about this problem is that there is a number in front of the x2. Lets start by "getting rid of it", or pulling it out of all the terms.

2x2+4x-240 = 2(x2+2x-120)

What you can see, is that you divide every term by 2 to get what is in the parenthesis above. For the rest of the problem, we just deal with what is in the parenthesis, so for now, we can forget about the 2, but do not forget to put it back in for your final answer.

Lets focus on: x2+2x-120

What we need to do is factor this. What we need to do is get it to look something like the following

x2+2x-120 = (x + __ )(x + __ ) so we just need to fill in the blanks.

What I do is start by listing all the factors of -120, and pair them up, so here they are below.

1, -120     2, -60     3, -40     4, -30      5, -24     6, -20     8, -15     10, -12

-1, 120     -2, 60     -3, 40     -4, 30      -5, 24     -6, 20     -8, 15     -10, 12

Now that we have listed all of the factors, we need to find the right factors. The correct factors will add to 2.

We can think logically, and without doing any math, we can eliminate any pairs of numbers that are really far away from each other because they will not result in 2 when added together. So this will leave us with:

10, -12 and -10, 12

So which one adds to 2?

10+ -12= -2      or      -10+12=2

So the correct pair is -10, 12.

So x2+2x-120 = (x + -10)(x + 12)=(x - 10)(x + 12)

But do not forget about the 2 from before! So now, we get:

2x2+4x-240 = 2(x2+2x-120) = 2(x - 10)(x + 12) = (2x - 20)(x + 12).

Thus, 2x2+4x-240 = 2(x - 10)(x + 12)    or     2x2+4x-240 = (2x - 20)(x + 12).

It will depend on your instructors preferences, but both answers are correct!

I hope this helped!

First factor out the greatest common factor (GCF), which in this case is 2.

2x2 + 4x - 240     ->     2(x2 + 2x - 120)

Now to factor the trinomial. Since the c term is negative, then one factor has a plus sign and the other has a minus sign, like this: (x + ?)(x - ?). Now we need to find two numbers, one positive and one negative, that add to +2 and multiply to -120. 10 and 12 work, so it's only a matter of putting them with the right sign. +10 and -12 add to -2, but -10 and +12 add to +2.

2x2 + 4x - 240     ->     2(x2 + 2x - 120)     ->     2(x + 12)(x - 10)

Hello Lord,

Well the first thing I'll factor out is 2.  Now it's

2(X2 + 2x - 120)

Now I'm looking for two numbers that have a product of 120 and a DIFFERENCE of 2.  I say difference because remember, these two numbers are going to have to multiply to -120.  To get a negative product, one has to be positive, one has to be negative.  Also, don't forget that when we foil, these numbers will each be multiplied by X and then added together.  Since once will be positive and the other negative, we want a difference of 2. 

Whew!  Enough talk.  Let's think now:  a product of 120 and a difference of two.  They need to be 2 apart and multiply to 120.  I know!  Ten and Twelve!  The Ten will be subtracted, the Twelve will be added so we get a positive 2 in the middle.

2(X + 12)(X - 10)  and that's fully factored. 

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