Factor: $- 6 z ^ { 3 } + 60 z ^ { 2 } - 144 z$
A) $- 6 z ( z - 6 ) ( z - 4 )$
B) $z ( z - 6 ) ( 6 z - 24 )$
C) $6 z ( z - 6 ) ( z - 4 )$
D) $- 6 ( z + 6 ) ( z - 4 )$
E) Nonfactorable over the integers

Question

Quizplus · Accepted Answer

To factor this expression, we first take out a common factor of $-6z$, giving us $$-6z(z^2-10z+24).$$ Now we need to factor the quadratic inside the parentheses. We can do this by looking for two numbers that multiply to $24$ and add up to $10$. These numbers are $6$ and $4$, so we can factor the quadratic as $$(z-6)(z-4).$$ Putting everything together, we have $$-6z(z-6)(z-4),$$ which matches answer choice $\boxed{	extbf{(A)}}$.

Factor −6z3+60z2−144z- 6 z ^ { 3 } + 60 z ^ { 2 } - 144 z−6z3+60z2−144z

Factor $- 6 z ^ { 3 } + 60 z ^ { 2 } - 144 z$