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Question

If the polynomial x4+x2+1 is divided by (x2), then the reminder is ?

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Solution

We know, the Remainder Theorem states that when we divide a polynomial f(x) by xc, then the remainder is f(c).

Here, the given polynomial is f(x)=x4+x2+1 which is divided by (x2), then we calculate f(2) to find the remainder as shown below:

f(2)=(2)4+(2)2+1=16+4+1=21.

Hence, by remainder theorem, when f(x)=x4+x2+1 is divided by (x2), the remainder obtained is 21.

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