Factor the expression. Factor out any greatest common factors first. $$4 x ^ { 3 } + 32$$
A) $4 ( x - 2 ) \left( x ^ { 2 } + 8 x + 4 \right)$
B) $4 ( x + 4 ) \left( x ^ { 2 } + 4 x + 4 \right)$
C) $2 ( x - 2 ) \left( x ^ { 2 } + 2 x + 4 \right)$
D) $4 ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$
E) $2 ( x + 4 ) \left( x ^ { 2 } + 4 x - 16 \right)$

Question

Quizplus · Accepted Answer

First, factor out the greatest common factor, which is 4, from the expression: $4(x^3 + 8)$. Then, recognize $x^3 + 8$ as a sum of cubes: $x^3 + 2^3$. The sum of cubes formula is $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. Applying this, we get $x^3 + 2^3 = (x + 2)(x^2 - 2x + 4)$. Therefore, the factored form is $4(x + 2)(x^2 - 2x + 4)$.

Factor the Expression 4x3+324 x ^ { 3 } + 324x3+32

Factor the Expression $4 x ^ { 3 } + 32$