Question

the distributive property can be applied to which expression to factor (12x^{3}-9x^{2}+4x - 3)?
(3(4x^{3}-1)-(9x^{2}+4x))
(4x(3x^{2}+1)-3(3x^{2}-1))
(3x(4x - 3)-(3 + 4x))
(3x^{2}(4x - 3)+1(4x - 3))

Explanation:

Step1: Expand Option 1

$3(4x^3 - 1) - (9x^2 + 4x) = 12x^3 - 3 - 9x^2 - 4x = 12x^3 - 9x^2 - 4x - 3$

Step2: Expand Option 2

$4x(3x^2 + 1) - 3(3x^2 - 1) = 12x^3 + 4x - 9x^2 + 3 = 12x^3 - 9x^2 + 4x + 3$

Step3: Expand Option 3

$3x(4x - 3) - (3 + 4x) = 12x^2 - 9x - 3 - 4x = 12x^2 - 13x - 3$

Step4: Expand Option 4

$3x^2(4x - 3) + 1(4x - 3) = 12x^3 - 9x^2 + 4x - 3$

Step5: Match to target expression

Compare expanded results to $12x^3 - 9x^2 + 4x - 3$

Answer:

D. $3x^2(4x - 3) + 1(4x - 3)$