To factor the trinomial \(x^2 - 11x + 28\), we need to find two numbers that multiply to \(28\) (the constant term) and add up to \(-11\) (the coefficient of the linear term).
The numbers that satisfy these conditions are \(-4\) and \(-7\) because:
\[ -4 \times -7 = 28 \] \[ -4 + (-7) = -11 \]
So, we can factor the trinomial as follows:
\[ x^2 - 11x + 28 = (x - 4)(x - 7) \]
Thus, the factored form of the trinomial is \((x - 4)(x - 7)\).