Factor \( x^{2}+13 x+36 \)

To factor the quadratic expression \( x^{2} + 13x + 36 \), follow these steps: 1. **Identify the coefficients:** - The quadratic is in the form \( ax^{2} + bx + c \), where: - \( a = 1 \) - \( b = 13 \) - \( c = 36 \) 2. **Find two numbers that multiply to \( c \) (36) and add up to \( b \) (13):** - List the pairs of factors of 36: - \( 1 \times 36 = 36 \) and \( 1 + 36 = 37 \) (Not 13) - \( 2 \times 18 = 36 \) and \( 2 + 18 = 20 \) (Not 13) - \( 3 \times 12 = 36 \) and \( 3 + 12 = 15 \) (Not 13) - \( 4 \times 9 = 36 \) and \( 4 + 9 = 13 \) (**This pair works**) 3. **Write the factored form:** - Using the numbers 4 and 9, the quadratic can be factored as: \[ x^{2} + 13x + 36 = (x + 4)(x + 9) \] **Final Answer:** \[ x^{2} + 13x + 36 = (x + 4)(x + 9) \]