Question

question 12 of 40
factor ( 3x^3 - 15x^2 + 18x ).

a. ( 3(x^2 - 2)(x - 3) )
b. ( 3x(x - 2)(x - 3) )
c. ( 3(x^2 + 2)(x - 3) )
d. ( 3x(x + 2)(x - 3) )

Explanation:

Step1: Factor out GCF

The GCF of $3x^3$, $-15x^2$, and $18x$ is $3x$.
$3x^3 -15x^2 +18x = 3x(x^2 -5x +6)$

Step2: Factor quadratic

Find two numbers: product=6, sum=-5 → -2 and -3.
$x^2 -5x +6 = (x-2)(x-3)$

Step3: Combine factors

$3x(x-2)(x-3)$

Answer:

B. $3x(x-2)(x-3)$