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Question
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
Solution
Let f(x) = x3 + 2x2 – kx + 4
x – 2 = 0 `\implies` x = 2
On dividing f(x) by x – 2, it leaves a remainder k.
∴ f(2) = k
(2)3 + 2(2)2 – k(2) + 4 = k
8 + 8 – 2k + 4 = k
20 = 3k
`k = 20/3 = 6(2)/3`
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