Factor.
-$4 \mathrm{k}^{3}+32$
A) $4(\mathrm{k}+2)\left(\mathrm{k}^{2}-2 \mathrm{k}+4\right)$
B) $4(\mathrm{k}+8)\left(\mathrm{k}^{2}-8 \mathrm{k}+16\right)$
C) $4(k+2)\left(k^{2}+2 k+4\right)$
D) $4(k-2)\left(k^{2}+2 k+4\right)$

Question

Quizplus · Accepted Answer

The expression $4k^3 + 32$ can be factored as $4(k^3 + 8)$, which is a sum of cubes. The sum of cubes formula is $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. Applying this formula with $a = k$ and $b = 2$, we get $4(k + 2)(k^2 - 2k + 4)$.