Question
Use the factor theorem to determine whether g(x) is a factor ofp(x) in each of the following cases:
p(x) = x3 + 3x2 + 3x + 1,g(x) = x + 2
Solution
p(x) = x3 + 3x2 + 3x + 1,g(x) = x + 2
g(x) = 0
⇒ x + 2 = 0 ⇒ x = -2
∴ Zero of g(x) is - 2.
Now, p(- 2)
= (- 2)3 + 3(- 2)2 + 3(- 2) + 1
= - 8 + 12 - 6 + 1 = - 1 ≠ 0
∴ By factor theorem, g(x) is not a factor of p(x).
