Question

if the polynomial f(x)=xpower 4-6xcube+16xsquare -25x+10 is divided by another polynomial xsquare -2x+k the remainder comes out be x + a find k and a

Answer 1

By dividing polynomials as per the demand of the question we get
(x^4)-6(x^3)+16(x^2)-25x+10= (x^2-2x+k)×(x^2-4x+8-k)+(2k-9)x+(k^2-8k+10)
Here,remainder----
(2k-9)x+(k^2-8k+10)=x+a
2k-9=1 & k^2-8k+10=a
K=5 and 5square-8×5+10=a
a=-5
Answer is k=5, a=-5