Ask AI: factor a²+11a+18

Sure! To factor the quadratic expression \(a^2 + 11a + 18\), you want to find two binomials of the form \((a + p)(a + q)\) where the product of \(p\) and \(q\) equals the constant term (18) and their sum equals the coefficient of the linear term (11). 1. First, identify the constant term: \(18\). 2. Next, identify the linear coefficient: \(11\). You need to find two numbers that multiply to 18 and add up to 11. Listing the factor pairs of 18: - \(1 \cdot 18 = 18\) and \(1 + 18 = 19\) - \(2 \cdot 9 = 18\) and \(2 + 9 = 11\) - \(3 \cdot 6 = 18\) and \(3 + 6 = 9\) The pair \(2\) and \(9\) multiply to 18 and add up to 11. So, the factors are: \[a^2 + 11a + 18 = (a + 2)(a + 9)\] Therefore, the factored form of the expression \(a^2 + 11a + 18\) is \((a + 2)(a + 9)\).