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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
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