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 meet these criteria are \( -7 \) and \( -4 \) since:
- \( -7 \times -4 = 28 \)
- \( -7 + -4 = -11 \)
Therefore, we can factor the trinomial as:
\[ (x - 7)(x - 4) \]
So, the factored form is \( (x - 7)(x - 4) \).