Home › Forums › Math questions › Algebra questions

Polynomial

Posted July 1st, 2008 by magaski
in

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 and a.Mention all the steps please.

‹ Factorise quadratic equation ›

Comments

answer

On July 2nd, 2008 Structure says:
$$x^4-6x^3+16x^2-25x+10=(x^2-2x+k)(x^2-4x+b)+x+a=x^4-6x^3+(b+8+k)x^2-(2b+4k-1)x+kb+a$$

k+b=8
kb+a=10
2b+4k-1=25
so k=5
b=3
a=-5

$$x^4-6x^3+16x^2-25x+10=(x^2-2x+5)(x^2-4x+3)+x-5$$

Back to top