(x + 2) is a factor of which one of the following?
- A. x^5 - 4x^4 - 3x^3 + 8x^2 - 14x + 12 ✓
- B. x^5 + 4x^4 - 3x^3 + 8x^2 - 14x + 12
- C. x^5 - 4x^4 + 3x^3 + 8x^2 - 14x + 12
- D. x^5 - 4x - 3x^3 + 8x^2 + 14x + 12
Correct Answer: A. x^5 - 4x^4 - 3x^3 + 8x^2 - 14x + 12
Explanation
By the Factor Theorem, if (x+2) is a factor, then evaluating the polynomial at x = -2 must yield 0. For the first option: (-2)^5 - 4(-2)^4 - 3(-2)^3 + 8(-2)^2 - 14(-2) + 12 = -32 - 64 + 24 + 32 + 28 + 12 = 0.
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