Tuesday, 9 April 2019

how to find the remainder when a polynomial p(x) is divided my another polynomial q(x)



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 x23x+2 is:



a) (2^1001)x+(2^100+2)




b) (2^100+1)x+(2^1002)



c) (2^1001)x+(2^1002)



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=(x23x+2)q(x)+ax+b. Now plug x=1 and x=2 to find a and b.


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