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