Use the factor theorem to determine whether g(x) is a factor ofp(x) in each of the following cases:
 p(x) = x³ - 4x² + x + 6, g(x) = x - 3

p(x) = x³ - 4x² + x + 6, g(x) = x - 3
g(x) = 0
⇒ x - 3 = 0 ⇒ x = 3
∴ Zero of g(x) is 3.
Now, p( 3)
= (3)³ - 4(3)² + 3 + 6
= 27 - 36 + 3 + 6 = 0
∴ By factor theorem, g(x) is a factor of p{x).