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Question

Find the remainder when x3+3x2+3x+1 is divided by x+π.


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Solution

Evaluate the remainder:

Given that the polynomial x3+3x2+3x+1 is divided by x+π.

Let Px=x3+3x2+3x+1

According to the remainder theorem, when a polynomial, P(x) is divided by a linear polynomial, xa, the remainder of that division will be equivalent to P(a).

Thus, if x3+3x2+3x+1 is divided by the linear polynomial x+π, the remainder of that division will be equivalent to P(-π).

Hence, the remainder

P(-π)=(-π)3+3(-π)2+3(-π)+1

=-π3+3π2-3π+1

Therefore, when x3+3x2+3x+1 is divided by x+π, we get the remainder -π3+3π2-3π+1.


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