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.