# exam preparation

• Nov 25th 2009, 11:57 PM
jameyt
exam preparation
Hi there,

can anyone help me with this question from my practice exam?

r(x) = (x^3 + x^2 + 2x) / x ( x - 1)

i need to write r(x) as p(x) + t(x)/q(x), for polynomials p,t and q with deg(t) < deg(q)

Thanks
• Nov 26th 2009, 12:14 AM
Arturo_026
Not sure if this is how you should do it, but it seems to make sense to me.

r(x) = (x^2 + x + 2)/(x-1)
r(x) = [(x^2 + x -2) +4]/(x-1)
r(x) = (x+2) + 4/(x-1)
• Nov 26th 2009, 12:23 AM
jameyt
i have the answer here:

just not sure how to get it........:

x + 2 + 4x / (x^2 - x)
• Nov 26th 2009, 12:25 AM
Arturo_026
Quote:

Originally Posted by jameyt
i have the answer here:

just not sure how to get it........:

x + 2 + 4x
x^2 - x

Is this what you mean: (x+2) + (4x)/(x^2 -x)
• Nov 26th 2009, 12:28 AM
jameyt
yes sorry
• Nov 26th 2009, 12:37 AM
Arturo_026
Ok, sorry, I made an error in my first answer.
So here it is again, It's basically the same process but this time I won't cross out the x at the beginning:

r(x) = [x(x^2 + x + 2)]/(x^2-x)
r(x) = [x[(x^2 + x -2) +2 +2]]/(x^2-x) .... notice I added and subtracted 2 to get a factorable form

r(x) = [x(x+2)(x-1)]/[x(x-1)] + 4x/(x^2-x) ... simplify

r(x) = (x+2) + 4x/(x^2-x)

Write it out so you can see the process better.