Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{3}-1000$
A) $(x-10)\left(x^{2}+100\right)$
B) $(\mathrm{x}+10)\left(\mathrm{x}^{2}-10 \mathrm{x}+100\right)$
C) $(x-10)\left(x^{2}+10 x+100\right)$
D) $(x+1000)\left(x^{2}-1\right)$

Question

Quizplus · Accepted Answer

The given polynomial $x^{3}-1000$ is a difference of cubes, which can be factored using the formula $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$. Here, $a=x$ and $b=10$, so the factored form is $(x-10)(x^{2}+10x+100)$.