Question

factor.
$y^2 + 7y + 12$

Explanation:

Step1: Find two numbers that multiply to 12 and add to 7.

We need two numbers \( a \) and \( b \) such that \( a \times b = 12 \) and \( a + b = 7 \). The numbers 3 and 4 satisfy this because \( 3 \times 4 = 12 \) and \( 3 + 4 = 7 \).

Step2: Factor the quadratic expression.

Using the numbers found, we can factor \( y^2 + 7y + 12 \) as \( (y + 3)(y + 4) \).

Answer:

\( (y + 3)(y + 4) \)