Factor by any method.
-$$20 z ^ { 6 } + 3 z ^ { 3 } - 9$$
A) $\left( 4 z ^ { 3 } + 3 \right) \left( 5 z ^ { 3 } - 3 \right)$
B) $\left( 5 z ^ { 3 } + 3 \right) \left( 4 z ^ { 3 } - 3 \right)$
C) $\left( 4 z ^ { 3 } + 1 \right) \left( 5 z ^ { 3 } - 9 \right)$
D) $20 \left( z ^ { 3 } - 3 \right) \left( z ^ { 3 } + 3 \right)$

Question

Quizplus · Accepted Answer

The given expression can be factored by grouping. First, notice that $20z^6$ and $3z^3$ can be grouped together, and $-9$ stands alone. The expression doesn't factor neatly into groups that share a common factor in the traditional sense, but we can look for a pattern that fits the form $(a+b)(c+d)$ where $ac=20z^6$, $ad+bc=3z^3$, and $bd=-9$. The correct factorization that meets these criteria is $(4z^3+3)(5z^3-3)$, which multiplies out to the original expression.

Factor by Any Method 20z6+3z3−920 z ^ { 6 } + 3 z ^ { 3 } - 920z6+3z3−9

Factor by Any Method $20 z ^ { 6 } + 3 z ^ { 3 } - 9$