Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$3 x ^ { 3 } - 12 x ^ { 2 } - 135 x$$
A) $3 \left( x ^ { 2 } - 9 x \right) ( x + 5 )$
B) $x ( x - 9 ) ( 3 x + 15 )$
C) $3 x ( x - 9 ) ( x + 5 )$
D) $x ( 3 x - 27 ) ( x + 5 )$

Question

Quizplus · Accepted Answer

We can factor out a common factor of 3x from all three terms to get:

$$3x^3 - 12x^2 - 135x = 3x(x^2 - 4x - 45)$$

Now we can factor the quadratic expression in the parentheses by grouping:

$$3x(x^2 - 4x - 45) = 3x(x - 9)(x + 5)$$

So the fully factored form is:

$$3x(x - 9)(x + 5)$$

Therefore, the best choice is C.

Factor Completely 3x3−12x2−135x3 x ^ { 3 } - 12 x ^ { 2 } - 135 x3x3−12x2−135x

Factor Completely $3 x ^ { 3 } - 12 x ^ { 2 } - 135 x$