Question

The value of k such that (x-5) divides the polynomial p(x)= x^3-6x^2+kx+30 exactly,is

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Answer 1

k = - 1

Explanation:

If (x - 5) is a factor of p(x) then p(5) = 0

p(5) = 5³ - 6(5)² + 5k + 30 = 0 , that is

125 - 150 + 5k + 30 = 0

5 + 5k = 0 ( subtract 5 from both sides )

5k = - 5 ( divide both sides by 5 )

k = - 1