Solve Polynomial Decomposition: -4x2 + 15x - 8/(x-1)3(x+2) | Step-by-Step Guide

[js14]

−4x2 + 15x − 8/
(x − 1)3(x + 2)

A/x+2 + B/x-1 + C/(x-1)^2 + D(x-1)^3 =

A(x-1) + B(x+2) + C(x-1)^3 + D(x-1)^2 =

(Ax-A) + (Bx+2B) + (Cx^3-3C^2+Cx-C) + (Dx^2-2Dx+D) =

(Cx^3) + (-3Cx^2+Dx^2) + (Ax+Bx+Cx-2Dx) + (-A+2B-C+D)

I know this isn't finished but I think i when wrong somewhere. can someone help me?

 

[cragar]

are you trying to do partial fractions?

 

[js14]

Yes. My class just started on it the other day and I think I am getting close but I am still a little confused.

 

[cragar]

your first couple of steps look good .
$$\frac{-4x^2+15x-8}{(x-1)^3(x+2)}=\frac{A}{x+2}+\frac{B}{x-1}+\frac{C}{(x-1)^2}+\frac{D}{(x-1)^3}$$
then multiply both sides by$$(x-1)^3(x+2)$$
then you can solve for D by plugging in x=1 to zero out the other terms
and then plug in x=-2 to solve for A
so A=2 D=1
to solve for B and C expand out those polynomials and then equate the coefficient of the correct powers of x to give you different equations.
so you will equal all the x cubed therms to 0 and the x squared to -4 ... etc.

 

[js14]

Thank you.

 

[cragar]

your welcome