Question

Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping? x2(4x + 1) – 2(4x + 1) x2(4x – 1) + 2(4x – 1) 4x2(x + 2) – 1(x + 2) 4x2(x – 2) – 1(x – 2)

Answer 1

It's the first choice

Answer 2

Looking at   4x3 + x2 – 8x – 2, I see immediately that x^2 can be factored out of the first 2 terms => 4x^2(x+1)
and -2 out of the last 2 terms => -2(4x+1).

Notice how the factor (4x+1) shows up twice.

We can factor this (4x+1) out, obtaining   (x^2 - 2) (4x+1).  These are the desired factors, found "by grouping."