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Question
Find the remainder when the polynomial f(x) = 2x4 - 6x3 + 2x2 - x + 2 is divided by x + 2.
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Solution
If x + 2 = 0
x = -2
f(x) = 2x4 - 6x3 + 2x2 - x + 2, ...[By remainder theorem]
f(-2) = 2(-2)4 - 6(-2)3 + 2(-2)2 - (-2) + 2
= 2(16) -6(-8) + 2(4) + 2 + 2
= 32 + 48 + 8 + 2 + 2 = 92
Hence, required remainder = 92.
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