Ask AI: factor n²-11n+10

To factor the quadratic expression \( n^2 - 11n + 10 \), we need to find two numbers that multiply together to give the constant term (10) and add together to give the coefficient of the linear term (-11). Let's denote these two numbers as \( a \) and \( b \). We need: 1. \( a \cdot b = 10 \) 2. \( a + b = -11 \) By inspecting the pairs of factors of 10: - \( 1 \) and \( 10 \) - Sum: \( 1 + 10 = 11 \) - \( -1 \) and \( -10 \) - Sum: \( -1 + (-10) = -11 \) - \( 2 \) and \( 5 \) - Sum: \( 2 + 5 = 7 \) - \( -2 \) and \( -5 \) - Sum: \( -2 + (-5) = -7 \) The pair that adds up to -11 is \(-1\) and \(-10\). Thus, the quadratic \( n^2 - 11n + 10 \) can be factored as: \[ (n - 1)(n - 10) \] So, the factored form of \( n^2 - 11n + 10 \) is: \[ (n - 1)(n - 10) \]