Question

Factor –8x3 – 2x2 – 12x – 3 by grouping. What is the resulting expression? A. (2x2 – 3)(4x + 1) b. (–2x2 – 3)(–4x + 1) c. (2x2 – 3)(–4x + 1) d. (–2x2 – 3)(4x + 1)

Answer 1

it's D
(–2x2 – 3)(4x + 1)

Answer 2

Consider the polynomial
`-8x^3 - 2x^2 - 12x - 3`. You can group first two terms and second two terms:

`-8x^3 - 2x^2 - 12x - 3= (-8x^3 - 2x^2 )+(- 12x - 3)`.

Find the common factors in both brackets:

• in brackets
  `(-8x^3 - 2x^2 )` the common factor is
  `-2x^2`;
• in brackets
  `(- 12x - 3)` the common factor is
  `-3`.

Then rewrite the polynomial as

`-8x^3 - 2x^2 - 12x - 3= (-8x^3 - 2x^2 )+(- 12x - 3) =-2x^2(4x+1)-3(4x+1)`.

Here you see that expression 4x+1 is common, then

`-8x^3 - 2x^2 - 12x - 3=-2x^2(4x+1)-3(4x+1)=(4x+1)(-2x^2-3).`.

Answer: correct choice is D.