i was solving the question from the book IIT FOUNDATION AND OLYMPIAD - X
and i was solving the problems of polynomials-III
. so on the page number 136, there is a question (question 17) given below:
The remainder when x^100 is divided by x2−3x+2 is:
a) (2^100−1)x+(−2^100+2)
b) (2^100+1)x+(−2^100−2)
c) (2^100−1)x+(−2^100−2)
d) none
as far as i tried to find the remainder, i tried long division method but it was getting more and more complicated, then i used systematic method of division but i can't get the corret option
what is the correct option. please explain me how did you find the remainder. thanks
and yes its answer is option (a)
Answer
Hint Write x100=(x2−3x+2)q(x)+ax+b. Now plug x=1 and x=2 to find a and b.
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