To factor the quadratic expression \( k^2 + 8k - 9 \), we need to find two numbers that multiply to \(-9\) (the constant term) and add to \(8\) (the coefficient of the linear term).
The numbers that satisfy these conditions are \(9\) and \(-1\) since:
- \(9 \times (-1) = -9\)
- \(9 + (-1) = 8\)
Now, we can factor the expression as follows:
\[ k^2 + 8k - 9 = (k + 9)(k - 1) \]
Thus, the factored form of \( k^2 + 8k - 9 \) is:
\[ \boxed{(k + 9)(k - 1)} \]