f(x) = x2+kx+6. If (x−2) is a factor of f(x), then the value of k = .
A
5
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B
-5
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C
4
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D
-4
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Solution
The correct option is B -5 According to the factor theorem, if (x−a) is a factor of a polynomial f(x), then f(a) = 0. Given, (x−2) is a factor of f(x), then f(2) = 0. ⇒ f(2) = 22+k×2+6=0 ⇒4+2k+6=0 ⇒2k=−10 ⇒k=−5