If x - 3 is a factor of the polynomial P(x) = 2x^3 - kx^2 + 5x - 6, what is the value of k?
Answer and explanation
Correct answer: D. 7
- Step 1: By the Factor Theorem, P(3) = 0. Step 2. P(3) = 2(27) - k(9) + 5(3) - 6 = 54 - 9k + 15 - 6 = 63 - 9k = 0. Step 3. 9k = 63 => k = 7. Answer: 7. Why not the others: k = -7 gives 54 + 63 + 9 != 0.
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