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Question
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
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Solution
Let f(x) = x3 + 3x2 – mx + 4
According to the given information,
f(2) = m + 3
(2)3 + 3(2)2 – m(2) + 4 = m + 3
8 + 12 – 2m + 4 = m + 3
24 – 3 = m + 2m
3m = 21
m = 7
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