Question

Select the correct answer.

Which expression represents -8x2 + 54x + 140 in factored form?

(x – 70)(-8x + 2)
(x + 1)(8x – 140)
(x – 8)(2x + 70)
(x + 2)(-8x + 70)

Answer 1

Start with what you can get rid of just by eyeballing it. All of the factors on the left have 1x as a given. So that means that on the second factor you need a minus 8x. That lets out B and C as answers.

You have 54x as the middle term. A is going to be huge on the middle term. Huge. -8x * 70 gives you - 560x. It's far too big. That let's out A. So we are going to focus on D.

(x + 2)(-8x + 70) = -8x^2 - 16x + 70x + 140

(x + 2)(-8x + 70) = -8x^2 + 56x + 140

So we have the answer. Notice how most of this question was done just by looking at the answers. Some of them were eliminated by vision alone. I recommend you try this with any math question. Use your eyes before a calculator, pencil and piece of paper.

Answer 2

-8x2 + 54x + 140

factor out a -2

-2(4x^2 -26x-70)

-2(4x-35) (x+2)

this is the completely factored form

distribute the -2

(-8x+70) (x+2)

Choice D