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Question

Find the remainder when x34x2+12x+7 is divided by x+12.

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Solution

Given, f(x)=x34x2+12x+7.

Here, f(x) is divided by (x+12).

Now, according to the remainder theorem, when f(x) is divided by (x+12), then the remainder is f(12).
Then,

f(12) =(12)34(12)2+12(12)+7
=(18)4(14)+12(12)+7
=(18)16+7

=(18)7+7

=18.

Hence, the remainder obtained is 18.

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