If (x + 1) is a factor of polynomial p(x) = x4 + 3x3 + 3x2 + x + 1, then p(−1) must be 0, otherwise (x + 1) is not a factor of this polynomial.
p(−1) = (−1)4 + 3(−1)3 + 3(−1)2 + (−1) + 1
= 1 − 3 + 3 − 1 + 1 = 1 As p(−1) ≠ 0,
Therefore, x + 1 is not a factor of this polynomial.