Question 378418: I am trying to figure out if the denominator of this fraction factors any lower than what it is. The fraction is 3x^3+x^2-27x-9/ 2x^3+9x^2-8x-15. I know that I can't factor by grouping because the groups in this polynomial in the denominator wouldn't have anything in common. I am stuck on this problem and don't know what else to try, please help!! Answer by solver91311(17059) (Show Source):
First use the Rational Roots Theorem which says that if
has a rational root then it must be of the form:
Where is an integer factor of and is an integer factor of
Using that, the only possible rational factors of
Use synthetic division to test these 16 trial divisors until you either find one that divides the original cubic polynomial evenly, leaving you with the successful trial divisor as one factor and a quotient consisting of a quadratic trinomial as another (and hopefully further factorable) factor, or you exhaust all of the possibilities and thereby determine that your denominator is prime.
If you need a refresher on Synthetic Division, see: