To factor the quadratic expression \( k^2 + 6k - 7 \), we look for two numbers that multiply to \(-7\) (the constant term) and add up to \(6\) (the coefficient of the linear term).
The numbers that satisfy these conditions are \(7\) and \(-1\), since:
\[ 7 \times (-1) = -7 \quad \text{and} \quad 7 + (-1) = 6. \]
We can use these numbers to factor the quadratic:
\[ k^2 + 6k - 7 = (k + 7)(k - 1). \]
Thus, the factored form of \( k^2 + 6k - 7 \) is:
\[ (k + 7)(k - 1). \]