Factor.
-$80 z ^ { 8 } + 108 z ^ { 5 } + 36 z ^ { 2 }$
A) $4 z ^ { 2 } \left( 5 z ^ { 3 } - 3 \right) \left( 4 z ^ { 3 } - 3 \right)$
B) $\left( 4 z ^ { 4 } + 4 \right) \left( 5 z ^ { 4 } + 3 \right)$
C) $4 z ^ { 2 } \left( 4 z ^ { 3 } + 3 \right) \left( 5 z ^ { 3 } + 3 \right)$
D) $4 \left( 4 z ^ { 6 } + 3 \right) \left( 5 z ^ { 2 } + 3 \right)$

Question

Quizplus · Accepted Answer

We can see that each term has a common factor of $4z^2$. Factoring this out, we get $4z^{2}(20z^6+27z^3+9)$. Now we can see that the expression inside the parentheses is a perfect square trinomial (similar to $x^2+6x+9$), which factors as $(ax^3+b)^2=a^2x^6+2abx^3+b^2$. In this case, we have $a=\sqrt{20}=2\sqrt{5}$ and $b=\sqrt{9}=3$, so the trinomial becomes $(2\sqrt{5}z^3+3)^2 = 20z^6+12\sqrt{5}z^3+9$.

Thus, we can write $4z^2(20z^6+27z^3+9) = 4z^2(2\sqrt{5}z^3+3)^2 = 4z^2 (4z^3+3)(5z^3+3)$, which is answer choice $\boxed{	extbf{(C)}}$.

Factor - 80z8+108z5+36z280 z ^ { 8 } + 108 z ^ { 5 } + 36 z ^ { 2 }80z8+108z5+36z2

Factor
- $80 z ^ { 8 } + 108 z ^ { 5 } + 36 z ^ { 2 }$