Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$2 x ^ { 3 } + 6 x ^ { 2 } - 36 x$$
A) $2 x ( x + 6 ) ( x + 3 )$
B) $2 x ( x + 6 ) ( x - 3 )$
C) $2 x ( x - 6 ) ( x + 3 )$
D) $2 x ( x - 6 ) ( x - 3 )$

Question

Quizplus · Accepted Answer

The first step in factoring is to look for a common factor among the terms. Here, 2x can be factored out. So, the given polynomial can be written as:
$$2x(x^2+3x-18)$$
Now, we need to factor the quadratic expression inside the parentheses. It can be written as:
$$x^2+3x-18=(x-3)(x+6)$$
Therefore, the complete factorization of the given polynomial is:
$$2x(x-3)(x+6)$$ which matches option B.

Factor Completely 2x3+6x2−36x2 x ^ { 3 } + 6 x ^ { 2 } - 36 x2x3+6x2−36x

Factor Completely $2 x ^ { 3 } + 6 x ^ { 2 } - 36 x$