To factor the quadratic expression \(x^2 - 9x + 20\) as the product of two binomials, we start by looking for two numbers that multiply to the constant term (20) and add to the linear coefficient (-9).
The numbers that satisfy these conditions are -4 and -5, since: \[ -4 \times -5 = 20 \quad \text{(multiply to 20)} \] \[ -4 + (-5) = -9 \quad \text{(add to -9)} \]
Now we can write the expression in factored form: \[ x^2 - 9x + 20 = (x - 4)(x - 5) \]
Thus, the factorization of \(x^2 - 9x + 20\) is: \[ \boxed{(x - 4)(x - 5)} \]