Question

question
factor.
$x^2 + 8x + 15$
answer attempts 1 out of 10

Explanation:

Step1: Find two numbers that multiply to 15 and add to 8.

We need two numbers \( m \) and \( n \) such that \( m \times n = 15 \) and \( m + n = 8 \). The numbers 3 and 5 satisfy this because \( 3\times5 = 15 \) and \( 3 + 5 = 8 \).

Step2: Rewrite the middle term and factor by grouping.

Rewrite the quadratic \( x^{2}+8x + 15 \) as \( x^{2}+3x+5x + 15 \).
Now, group the first two terms and the last two terms: \( (x^{2}+3x)+(5x + 15) \).
Factor out the greatest common factor from each group: \( x(x + 3)+5(x + 3) \).
Then, factor out the common binomial factor \( (x + 3) \): \( (x + 3)(x + 5) \).

Answer:

\( (x + 3)(x + 5) \)