To factor the polynomial \( x^5 - x^4 + 3x - 3 \), we can start by checking for rational roots using the Rational Root Theorem. The possible rational roots are factors of the constant term (-3) divided by factors of the leading coefficient (1), which gives us possible roots of \( \pm 1, \pm 3 \).
Let's test some of these values:
1. Testing \( x = 1 \):
\[
f(1) = 1^5 - 1^4 + 3(1) - 3 = 1 - 1 + 3 - 3 = 0
\]
Thus, \( x = 1 \) is a