QQuestion
If x − 2 is a factor of x3 − kx − 12, then the value of k is:
(a) 3
(b) 2
(c) −2
(d) −3
✓Answer
(c) −2
Explanation:
x – 2 is a factor of x3 – kx – 12
⇒ x – 2 = 0
⇒ x = 2
By the factor theorem, f(2) = 0.
⇒ 23 − 2k − 12 = 0
⇒ 8 − 2k − 12 = 0
∴ −2k = 4, therefore k = −2.
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