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Question
For what value of a is (x − 5) a factor of x3 − 3x2 + ax − 10?
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Solution
Let f(x) = x3 − 3x2 + ax − 10 be the given polynomial.
By factor theorem, (x-5)is the factor of f(x), if f (5) = 0
Therefore,
`f(5) = (5)^3 - 3(5)^2 + a(5) - 10 = 0`
` 125 - 75 + 5a - 10 = 0 `
`5a = -40`
a = -8
Hence, a = − 8.
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