# The remainder R obtained by dividing x100 by x²-3x+2 is a polynomial of degree less than 2. then r may be written as ?

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by kunal322

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by kunal322

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The Brainliest Answer!

When p(x) is divided by q(x), then by division algorithm there exists Q(x) and R(x) such that

p(x)=q(x)+r(x)

x^100=(x-1)(x-2)q(x)+(Ax+B)

put x=1 and x=2

1=A+B and 2^100=2A+B

by solving

A=2^100-1

B=2-2^100

then rem will be...

(2^100-1)x+(2-2^100)