Hi Sniperpro
The question asks you to find the root of (x^3-3x^2+3x-9), then you factorize the denominator. Finally, find the partial fraction decomposition of g(x)
so the question has two parts and goes like this:
1) use long division to turn the rational function:
f(x)=(2x^4-5x^3-9x-12)/(x^3-3x^2+3x-9)
into the sum of a polynomial and a proper rational function g(x).
so i did this and got the answer, then i got stuck on part two when it asked:
2) Look for a small integer root of the denominator of f(x); and use this to find the partial fraction decomposition of g(x)
help please!? i don't know what it's asking me to do.
should be ...
note that the denominator of the original fraction (and the last term above) equals 0 when x = 3 ... according to the factor theorem, that makes (x-3) a factor ...
the last question also wants a partial fraction decomposition of the last term ...
your last task is to find the values of the constants A , B, and C.
Hi Sniperpro
As skeeter said :
So, and you can factorize x^3 - 3x^2 + 3x - 9.note that the denominator of the original fraction (and the last term above) equals 0 when x = 3 ... according to the factor theorem, that makes (x-3) a factor ...
x^3 - 3x^2 + 3x - 9 = (x-3)(x^2 + 3) as skeeter has pointed out ^^