Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following cases: p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2

(ii) p(x) = x³ + 3x² + 3x + 1 and g(x) = x + 2
Putting x + 2 = 0, we get, x = 2
Using remainder theorem, when p(x) = x³ + 3x² + 3x + 1 is divided by (g(x) = x + 2, remainder is given by p(-2)
= (-2)³ + 3(-2)² + 3(-2) + 1
= -8 + 12 – 6 + 1
= -1
Since, remainder p(-2) ≠ 0, hence g(x) is not a factor of p(x).