To factor the quadratic expression \( z^2 - 5z + 6 \), we need to find two numbers that multiply to \( +6 \) (the constant term) and add up to \( -5 \) (the coefficient of the \( z \) term).
The two numbers that satisfy these conditions are \( -2 \) and \( -3 \).
So we can express the quadratic as:
\[ (z - 2)(z - 3) \]
Thus, the factored form of \( z^2 - 5z + 6 \) is:
\[ (z - 2)(z - 3) \]