What is the quotient of d-2 divided by d^4-6d^3+d+17?

1 Answer
Jul 3, 2017

The quotient is =(d^3-4d^2-8d-15)

Explanation:

Let's perform the long division

d-2color(white)(aaaa)|d^4-6d^3+0d^2+d+17color(white)(aa)|d^3-4d^2-8d-15

color(white)(aaaaaaaaaa)d^4-2d^3

color(white)(aaaaaaaaaaa)0-4d^3+0d^2

color(white)(aaaaaaaaaaaaa)-4d^3+8d^2

color(white)(aaaaaaaaaaaaaa)-0-8d^2+d

color(white)(aaaaaaaaaaaaaaaaa)-8d^2+16d

color(white)(aaaaaaaaaaaaaaaaaaa)-0-15d+17

color(white)(aaaaaaaaaaaaaaaaaaaaaaa)-15d+30

color(white)(aaaaaaaaaaaaaaaaaaaaaaaaa)-0-13

Therefore,

(d^4-6d^3+d+17)/(d-2)=d^3-4d^2-8d-15-13/(d-2)

The remainder is =-13 and the quotient is =(d^3-4d^2-8d-15)