Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$y z ^ { 3 } + 512 y$$
A) $( y z + 8 ) \left( z ^ { 2 } - 8 z + 64 y \right)$
B) $y ( z + 8 ) \left( z ^ { 2 } + 64 \right)$
C) $y ( z - 8 ) \left( z ^ { 2 } + 8 z + 64 \right)$
D) $y ( z + 8 ) \left( z ^ { 2 } - 8 z + 64 \right)$

Question

Quizplus · Accepted Answer

We can factor out y from the given polynomial to get $y(z^3+512)$. Notice that $z^3+512$ is the sum of cubes, which can be factored as $(z+8)(z^2-8z+64)$. Therefore, the polynomial can be factored as $y(z+8)(z^2-8z+64)$. The correct choice is (D).

Factor Completely yz3+512yy z ^ { 3 } + 512 yyz3+512y

Factor Completely $y z ^ { 3 } + 512 y$