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What is the value of k such that x³-x²+kx-30 :(x-5) has a remainder of zero

1 Answer

1 vote

Answer:

k = - 14

Explanation:

By the remainder theorem

if a function f(x) is divided by (x - a) then the remainder is f(a)

given a remainder of zero when divided by (x - 5) , then

substituting x = 5 into the polynomial and equating to zero

x³ - x² + kx - 30 , gives

5³ - 5² + 5k - 30 = 0

125 - 25 + 5k - 30 = 0

5k + 70 = 0 ( subtract 70 from both sides )

5k = - 70 ( divide both sides by 5 )

k = - 14

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