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Question

2 3 P() = 0 O x + 1 is a factor of P(x) O x + 1 is not a factor of P(x) X 4 $ 5 6 7 3 Use the Factor Theorem to determine whether x + 1 is a factor of P (x) = − xª¹ − x³ + 2x + 4. Specifically, evaluate P at the proper value, and then determine whether x + 1 is a factor. 8 00

Answer

To utilize the Factor Theorem and assess if x + 1 is a factor of P(x) = -x^4 - x^3 + 2x + 4, we must compute P (-1). Should the outcome be zero, x + 1 is without a doubt a factor of P(x); but if it is not, then x + 1 is not a factor of P(x). By substituting x = -1 into the P(x) function, we get: P(-1) = (-1)^4 + (-1)^3 + 2(-1) + 4 = 1 + -1 + -2 + 4 = 2. Seeing as P(-1) is not zero, we can deduce that x + 1 is not a factor of P(x).