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

(i) p(x) = 2x³ + x² – 2x – 1 and g(x) = x + 1
putting x + 1 = 0, we get, x = -1
Using remainder theorem, when p(x) = 2x³ + x² – 2x – 1 is divided by g(x) = x + 1, remainder is given by p(-1)
= (-1)³ + (-1)² + (-1) + 1
= -1 + 1 – 1 + 1 = 0
Since, remainder p(-1) = 0, hence g(x) is factor of p(x).