If (x + 2) is a factor of the polynomial P(x) = x³ + kx² - 4x - 12, what is the value of k?

A k = 1

B k = 2

C k = 3

D k = 4

✓ Correct Answer: Option C

By the Factor Theorem, if (x + 2) is a factor, then P(-2) = 0. Substitute x = -2 into P(x): (-2)³ + k(-2)² - 4(-2) - 12 = 0. This simplifies to -8 + 4k + 8 - 12 = 0, so 4k - 12 = 0, which means k = 3.

💡 Why is C) the correct answer?

The correct answer to the question "If (x + 2) is a factor of the polynomial P(x) = x³ + kx² - 4x - 12, what is the value of k?" is Option C: k = 3.

The other options — A) k = 1, B) k = 2, D) k = 4 — are incorrect for this CLEP Exam Prep question. As explained above: By the Factor Theorem, if (x + 2) is a factor, then P(-2) = 0. Substitute x = -2 into P(x): (-2)³ + k(-2)² - 4(-2) - 12 = 0. This simplifies to -8 + 4k + 8 - 12 = 0, so 4k - 12 = 0, which means k = 3.

📚 About This CLEP Exam Prep Practice Question

This 2-level CLEP Exam Prep question from the College Algebra topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free CLEP Exam Prep practice test or use flashcards for spaced repetition review.

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If (x + 2) is a factor of the polynomial P(x) = x³ + kx² - 4x - 12, what is the value of k?

✓ Correct Answer: Option C

📚 About This CLEP Exam Prep Practice Question

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