Trying to find the right answer to this..

p(x) = x 3 + 3x 2 + 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).

Coordinate Geometry

Question

Wired Faculty App

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

Answer

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).