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!