Question

the remainder when x^2014 is divided by x^2 -3x + 2 1s​

Answer 1

The degree of the reminder should be less than the degree of the divider

Degree of the divider is 2. Therefore the degree of the reminder would be 1.  

Let the reminder be of the form Ax+B and the quotient be f(x)

x2015+x2014+2015=f(x)⋅(x2−1)+Ax+B

When x = 1 :1+1+2015=0+A+B⟹A+B=2017

When x = -1 :−1+1+2015=0−A+B⟹B−A=2015

⟹2B=4032⟹B=2016;A=1