Factor.
-$3 x ^ { 5 } - 21 x ^ { 4 } + 36 x ^ { 3 }$
A) $3 x ^ { 3 } ( x - 3 ) ( x + 4 )$
B) $3 x ^ { 3 } ( x + 3 ) ( x - 4 )$
C) $3 x ^ { 3 } ( x - 3 ) ( x - 4 )$
D) $3 x ^ { 3 } ( x + 3 ) ( x + 4 )$

Question

Quizplus · Accepted Answer

We can use the factor theorem to factor the expression. Notice that if we set $x=3$, the first two terms cancel out, and if we set $x=4$, the last two terms cancel out. Therefore, we can factor out $(x-3)$ and $(x-4)$. 
$$3x^5-21x^4+36x^3=3x^3(x^2-7x+12)=3x^3(x-3)(x-4)$$
The correct answer is choice C, as it correctly factors the expression.

Factor - 3x5−21x4+36x33 x ^ { 5 } - 21 x ^ { 4 } + 36 x ^ { 3 }3x5−21x4+36x3

Factor
- $3 x ^ { 5 } - 21 x ^ { 4 } + 36 x ^ { 3 }$