The expression \( x^2 - 5x + 4 \) is a quadratic polynomial. To factor this quadratic expression, we look for two numbers that multiply to the constant term (4) and add up to the coefficient of the linear term (-5).

The numbers that satisfy these conditions are -1 and -4 because:
- (-1) * (-4) = 4
- (-1) + (-4) = -5

Therefore, we can factor the quadratic expression as follows:
\[ x^2 - 5x + 4 = (x - 1)(x - 4) \]

So, the factored form of \( x^2 - 5x + 4 \) is \( (x - 1)(x - 4) \).