Long Division...3

Section 2.3
Question 24

How can I use long division to answer 24? The denominator is a binomial squared.

 

(2x^3-4x^2-15x+5)/(x-1)^2

Expand the divisor: (x-1)^2=x^2-2x+1

..................(2x
(x^2-2x+1)|2x^3-4x^2-15x+5
...................2x^3-4x^2+2x................subtract
....................................-17x..........bring 5 down
....................................-17x+5-> reminder

(2x^3-4x^2-15x+5)/(x-1)^2=2x +(-17x+5)/(x-1)^2

or
2x^3-4x^2-15x+5=2x(x-1)^2 +(-17x+5)

 

I would you to show the work on paper. Take a picture and upload it here for clarity.