Question
Use the factor theorem to determine whether g(x) is a factor ofp(x) in each of the following cases:
p(x) = 2x3 + x2 - 2x - 1, g(x) = x + 1
Solution
p(x) = 2x3 + x2 - 2x - 1, g(x) = x + 1
g(x) = 0
⇒ x + 1 = 0 ⇒ x = - 1
∴ Zero of g(x) is - 1.
Now, p(- 1)
= 2(- 1)3 + (- 1)2 - 2(- 1) - 1
= - 2 + 1 + 2 - 1 = 0
∴ By factor theorem, g(x) is a factor of p(x).
