Consider the polynomial [tex] -8x^3 - 2x^2 - 12x - 3 [/tex]. You can group first two terms and second two terms:
[tex] -8x^3 - 2x^2 - 12x - 3= (-8x^3 - 2x^2 )+(- 12x - 3) [/tex].
Find the common factors in both brackets:
- in brackets [tex] (-8x^3 - 2x^2 ) [/tex] the common factor is [tex] -2x^2 [/tex];
- in brackets [tex](- 12x - 3) [/tex] the common factor is [tex] -3 [/tex].
Then rewrite the polynomial as
[tex] -8x^3 - 2x^2 - 12x - 3= (-8x^3 - 2x^2 )+(- 12x - 3) =-2x^2(4x+1)-3(4x+1) [/tex].
Here you see that expression 4x+1 is common, then
[tex] -8x^3 - 2x^2 - 12x - 3=-2x^2(4x+1)-3(4x+1)=(4x+1)(-2x^2-3). [/tex].
Answer: correct choice is D.
