Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(i) 
(ii)
(iii) 
(i) If g (x) = x + 1 is a factor of given polynomial p (x), p (-1) must be zero
p (x) = 2x3 + x2 – 2x – 1
p (-1) = 2 (-1)3 + (-1)2 – 2 (-1) – 1
= 2 (-1) + 1 + 2 – 1 = 0
Hence, g (x) = x + 1 is a factor of given polynomial
(ii) If g (x) = x + 2 is a factor of given polynomial p (x), p (-2) must be zero
p (x) = x3 + 3x2 + 3x + 1
p (-2) = (-2)3 + 3(-2)2 + 3 (-2) + 1
= -8 + 12 - 6 + 1 = -1
As, p (-2) ≠ 0
Hence, g (x) = x + 2 is not a factor of given polynomial
(iii) If g (x) = x – 3 is a factor of given polynomial p (x), p (3) must be zero
p (x) = x3 – 4x2 + x + 6
p (3) = (3)3 – 4 (3)2 + 3 + 6
= 27 – 36 + 9 = 0
Therefore, g(x) = x – 3 is a factor of the given polynomial