What is the remainder when P(x) = 2x^3 - 3x^2 + x - 5 is divided by x+1?

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Multiple Choice

What is the remainder when P(x) = 2x^3 - 3x^2 + x - 5 is divided by x+1?

Explanation:
Use the Remainder Theorem: dividing by a linear factor x − c leaves a remainder equal to P(c). Here the divisor is x+1 = x − (−1), so c = −1. Evaluate P at −1: P(−1) = 2(−1)^3 − 3(−1)^2 + (−1) − 5 = −2 − 3 − 1 − 5 = −11. So the remainder is −11. Since it’s not zero, x+1 is not a factor.

Use the Remainder Theorem: dividing by a linear factor x − c leaves a remainder equal to P(c). Here the divisor is x+1 = x − (−1), so c = −1. Evaluate P at −1: P(−1) = 2(−1)^3 − 3(−1)^2 + (−1) − 5 = −2 − 3 − 1 − 5 = −11. So the remainder is −11. Since it’s not zero, x+1 is not a factor.

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