## Precalculus Textbook 8th Edition Section 2.4 Exercise 24 Solution

**Question**:

Use the factor theorem to determine whether the first polynomial (x + 1) is a factor of the second polynomial 2x^{10} – x^{9} + x^{8} + x^{7} + 2x^{6} – 3.

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**Solution**:

Given polynomial is f(x) = 2x^{10} – x^{9} + x^{8} + x^{7} + 2x^{6} – 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 2x^{10} – x^{9} + x^{8} + x^{7} + 2x^{6} – 3.

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