Questions: Factor the expression. y^2+13y+36=

Transcript text: Factor the expression. \[ y^{2}+13 y+36= \]

Solution

Solution Steps

To factor the quadratic expression \( y^2 + 13y + 36 \), we need to find two numbers that multiply to 36 (the constant term) and add up to 13 (the coefficient of the linear term). Once we find these numbers, we can express the quadratic as a product of two binomials.

Step 1: Identify the Quadratic Expression

We start with the quadratic expression given by \[ y^2 + 13y + 36. \]

Step 2: Factor the Expression

To factor the expression, we need to find two numbers that multiply to \(36\) (the constant term) and add up to \(13\) (the coefficient of the linear term). The numbers \(4\) and \(9\) satisfy these conditions since: \[ 4 \times 9 = 36 \quad \text{and} \quad 4 + 9 = 13. \]

Step 3: Write the Factored Form

Using the numbers found, we can express the quadratic as a product of two binomials: \[ y^2 + 13y + 36 = (y + 4)(y + 9). \]