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Question
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
Solution
Let p(x) = x3 – 2mx2 + 16
Since, p(x) is divisible by (x + 2), then remainder = 0
P(–2) = 0
⇒ (–2)3 – 2m(–2)2 + 16 = 0
⇒ – 8 – 8m + 16 = 0
⇒ 8 = 8m
m = 1
Hence, the value of m is 1.
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