Question

I am trying to get the polynomial;
x^7+2x^6+3x^5+4x^4+6x^3+6x^2+7x+8
divided by;
x^5-2x^4-3x^3+5x^2+2x-3

into a partial fraction form so that I can create a system of equations to solve for. So far, after dividing I have
(x+1)(x-1)^2, and (x^2-x-3) as factors along with an remainder ype thing of x^2+4x+14. This gives me
A/(x+1)+ B/(x-1)+ C/(x-1)^2+ Dx+E/(x^2-x-3)
I don't know if this is right, and need help from here.
Thanks

Answer 1

Bobpursley already answered your question. What is it that you do not understand about his answer?

Also -- please don't keep posting the same question -- even under different names.

Answer 2

I don't understand how to convert the partial fractions into a system

Answer 3

Jo or John
very messy problem
your denominator is factored correctly
your answer to your long division is indeed x^2 + 4x + 14 but you don't say what that remainder is, because it is the remainder that you have to work with.

so you are working with

remainder/[(x+1)(x-1)^2(x^2-x-3)
= A/(x+1)+ B/(x-1)+ (Cx+D)/(x-1)^2+ (Ex+F)/(x^2-x-3)

notice I changed the numerators of your last two fractions, because they have a quadratic denominator.

I now want you to watch this video

(Broken Link Removed)

beginning at time 16:00 he starts a problem very similar to yours