Solve the following quadratic function by factoring. \[ \begin{array}{l}f(x)=x^{2}-11 x+24 \\ x=[?] \\ \text { Enter the smallest solution first. }\end{array} \]

To solve the quadratic function \( f(x) = x^2 - 11x + 24 \) by factoring, we need to find two numbers that multiply to \( 24 \) (the constant term) and add up to \( -11 \) (the coefficient of \( x \)). The numbers that satisfy this are \( -3 \) and \( -8 \). We can then factor the expression as follows: \[ f(x) = (x - 3)(x - 8) \] To find the solutions, we set each factor equal to zero: 1. \( x - 3 = 0 \) ⇒ \( x = 3 \) 2. \( x - 8 = 0 \) ⇒ \( x = 8 \) Thus, the solutions are \( x = 3 \) and \( x = 8 \). Entering the smallest solution first, we have: \[ x = 3, 8 \]