Remainder when x^4+x^3-2x^2+x+1 is divided by x -1 .

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2. Polynomials

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Find the remainder when $x^4+x^3-2x^2+x+1$ is divided by $x -1$.

A

$2$

B

$3$

C

$4$

D

$5$

Solution

Here, $p(x)=x^4+x^3-2x^2+x+1$, and and the zero of $x -1$ is $1.$

So, $p(1)=(1)^{4}+(1)^{3}-2(1)^{2}+1+1$

$= 2$

So, by the Remainder Theorem, $2$ is the remainder when $x^{4}+x^{3}-2 x^{2}+x+1$ is divided by $x-1$.

Standard 9

Mathematics

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