To factor the quadratic expression \( p^2 - 9p - 22 \), we need to find two numbers that multiply to \(-22\) (the constant term) and add up to \(-9\) (the coefficient of the linear term \(p\)).
The two numbers that fit these criteria are \(-11\) and \(2\), since:
\[ -11 \times 2 = -22 \] \[ -11 + 2 = -9 \]
Now we can express the quadratic in factored form:
\[ p^2 - 9p - 22 = (p - 11)(p + 2) \]
Thus, the factored form of \( p^2 - 9p - 22 \) is:
\[ (p - 11)(p + 2) \]