If the polynomial, x^4 - 6x^3 + 16x^2 - 25x + 10 is divided by another polynomial x^2 - 2x + k, the remainder comes out to be x + a, find k + a, please work the complete solution instead of giving simply an answer.

Answer 1

by using long division,
divide x^4-6x^3+16x^2-25x+10with x^2-2x+k,
then you will find:
remainder=(-9+2k)x +10-8k+k^2
comparing with x + a,
-9+2k=1,k=5
a=10-8k+k^2,a=-5

therefore k + a=5-5=0