The problem asks to factor the polynomial $2x^2 + 20x + 18$. First, factor out the greatest common factor from each term. Then, factor the remaining polynomial.

1. Problem Description

The problem asks to factor the polynomial $2x^2 + 20x + 18$. First, factor out the greatest common factor from each term. Then, factor the remaining polynomial.

2. Solution Steps

First, we identify the greatest common factor (GCF) of the coefficients 2, 20, and

1

8. The GCF is

2. Factoring out 2 from the polynomial gives:

$2(x^2 + 10x + 9)$

Next, we need to factor the quadratic expression $x^2 + 10x + 9$. We are looking for two numbers that multiply to 9 and add up to

1

0. These numbers are 1 and

9. Therefore, we can factor the quadratic as $(x+1)(x+9)$.

So, the complete factorization of the original polynomial is:

$2(x+1)(x+9)$

3. Final Answer

$2(x+1)(x+9)$