Trying to find the right answer to this..

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

Coordinate Geometry

Question

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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

Answer

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).