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Question
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
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Solution
Let f(x) = 2x3 + 3x2 – kx + 5
Using remainder theorem,
f(2) = 7
∴ 2(2)3 + 3(2)2 – k(2) + 5 = 7
`\implies` 2(8) + 3(4) – k(2) + 5 = 7
`\implies` 16 + 12 – 2k + 5 = 7
`\implies` 2k = 16 + 12 + 5 – 7
`\implies` 2k = 26
`\implies` k = 13
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