To factor the quadratic expression \(q^2 - 11q + 24\), we need to find two numbers that multiply to the constant term (24) and add up to the coefficient of the linear term (-11).
The numbers that meet these criteria are -3 and -8, since:
- \(-3 \times -8 = 24\)
- \(-3 + -8 = -11\)
Using these numbers, we can factor the expression as follows:
\[ q^2 - 11q + 24 = (q - 3)(q - 8) \]
Thus, the factored form of \(q^2 - 11q + 24\) is \((q - 3)(q - 8)\).