Remainder obtained by dividing x(100) by x(2)-3x+2

Let p ( x ) = x ¹⁰⁰ and q ( x ) = x ² – 3 x + 2 = ( x – 1) ( x – 2)

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

Therefore, remainder 

now this is a gud question!!!

let

x¹⁰⁰ = P(x)(x-2)(x-1) + remainder

here P(x) is a polynomial function and remainder is of the for kx+c

remainder is liner as the degree should be less than 2 (i.e. of the divisor)

put x=2 nd x=1 in succesion to get two equations

2¹⁰⁰ = 2k +c  .......(i)

1 = k+c  ...... (ii)

solving them we get

k = 2¹⁰⁰  -1

and c= 2 - 2¹⁰⁰

hence your remainder is:

(2¹⁰⁰ -1)x   + (2  - 2¹⁰⁰)

Hope you liked it!! coZ i did..

divide it na polynomial diviion