Question

factor completely.
$30x^2 + 55x + 15$

select the correct choice below and, if necessary, fill in any answer box within your choice.

a. $30x^2 + 55x + 15 = \square$

b. $30x^2 + 55x + 15$ is prime.

Explanation:

Step1: Factor out GCF

First, find the greatest common factor (GCF) of 30, 55, and 15, which is 5.
$30x^2 + 55x + 15 = 5(6x^2 + 11x + 3)$

Step2: Factor quadratic trinomial

Factor $6x^2 + 11x + 3$ by finding two numbers that multiply to $6\times3=18$ and add to 11 (these numbers are 9 and 2). Split the middle term and factor by grouping:
$6x^2 + 9x + 2x + 3 = 3x(2x + 3) + 1(2x + 3) = (3x + 1)(2x + 3)$

Step3: Combine factors

Substitute the factored quadratic back into the expression from Step1.
$5(3x + 1)(2x + 3)$

Answer:

A. $30x^2 + 55x + 15=5(3x+1)(2x+3)$