Factor.
-$$12 z ^ { 6 } + 38 z ^ { 4 } + 20 z ^ { 2 }$$
A) $2 z ^ { 2 } \left( 3 z ^ { 2 } - 2 \right) \left( 2 z ^ { 2 } - 5 \right)$
B) $2 \left( 2 z ^ { 4 } + 5 \right) \left( 3 z ^ { 2 } + 2 \right)$
C) $\left( 4 z ^ { 3 } + 10 \right) \left( 3 z ^ { 3 } + 2 \right)$
D) $2 z ^ { 2 } \left( 2 z ^ { 2 } + 5 \right) \left( 3 z ^ { 2 } + 2 \right)$

Question

Quizplus · Accepted Answer

We can factor out $2z^2$ from each term to get $2z^2(6z^4+19z^2+10)$. Now we can factor the expression inside the parentheses. We can substitute $y=z^2$ to simplify the expression: $6y^2+19y+10$. Then we can factor this as $(3y+2)(2y+5)$. Substituting back $z^2$ for $y$, we get $2z^2(3z^2+2)(2z^2+5)$ as the final factored form. Therefore, the answer is $\boxed{	extbf{(D)}}$.

Factor - 12z6+38z4+20z212 z ^ { 6 } + 38 z ^ { 4 } + 20 z ^ { 2 }12z6+38z4+20z2

Factor
- $12 z ^ { 6 } + 38 z ^ { 4 } + 20 z ^ { 2 }$