Precalculus Textbook 8th Edition Section 2.4 Exercise 24 Solution

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Question:

Use the factor theorem to determine whether the first polynomial (x + 1) is a factor of the second polynomial 2x¹⁰ – x⁹ + x⁸ + x⁷ + 2x⁶ – 3.

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Solution:

Given polynomial is f(x) = 2x¹⁰ – x⁹ + x⁸ + x⁷ + 2x⁶ – 3

First polynomial is (x + 1). Then x + 1 = 0 ⇒ x = -1

Now, put x = -1 in f(x).

f(-1) = 2(-1)¹⁰ – (-1)⁹ + (-1)⁸ + (-1)⁷ + 2(-1)⁶ – 3

⇒ f(-1) = 2 + 1 + 1 – 1 + 2 – 3

⇒ f(-1) = 2

Since f(-1) is NOT zero, then first polynomial (x + 1) is NOT a factor of the second polynomial 2x¹⁰ – x⁹ + x⁸ + x⁷ + 2x⁶ – 3.

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