Question

first factor out the greatest common factor from each term. then factor the remaining polynomial.
3x² + 9x - 54
select the correct choice below and fill in any answer box within your choice.
a. 3x² + 9x - 54 =

b. 3x² + 9x - 54 is prime.

Explanation:

Step1: Factor out GCF

Identify the greatest common factor (GCF) of $3x^2$, $9x$, and $-54$, which is 3.
$3x^2 + 9x - 54 = 3(x^2 + 3x - 18)$

Step2: Factor quadratic polynomial

Find two numbers that multiply to $-18$ and add to $3$ (these numbers are 6 and $-3$), then factor the quadratic.
$x^2 + 3x - 18 = (x + 6)(x - 3)$

Step3: Combine factors

Substitute the factored quadratic back into the expression.
$3(x^2 + 3x - 18) = 3(x + 6)(x - 3)$

Answer:

A. $3x^2 + 9x - 54 = 3(x + 6)(x - 3)$