Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(i) p(x) = 2x³ + x² - x - 1, g(x) = x + 1
(ii) p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2
(iii) p(x) = x³ - x² + x + 6, g(x) = x - 3

(i) Apply factor theorem
x + 1 = 0
So x = -1
2x³ + x² - x - 1
Replace x by -1, we get
2(-1)³ + (-1)² - (-1) - 1 = -2 + 1 + 1 - 1 = -1
Reminder is -1
so that x + 1 is not a factor of 2x³ + x² - x - 1
(ii) Apply factor theorem
x + 2 = 0
So x = -2
x³ + 3x² + 3x + 1
Replace x by -2, we get
(-2)³ + 3(-2)² + 3(-2) + 1 = -8 + 12 - 6 + 1 = -1
Reminder is -1
so that x + 2 is not a factor of x³ + 3x² + 3x + 1
(iii) Apply factor theorem
x - 3 = 0
So x = 3
x³ - x² + x + 6
Replace x by 3, we get
(3)³ - (3)² + (3) + 6 = 27 - 9 + 3 + 6 = 27
Reminder is 27
so that x - 3 is not a factor of x³ - x² + x + 6