solve x^5-3x^3+2x^2-3>0

Question

can i solve this inequality without a graphing calculator?

Answer 1

The best way is to use long division or synthetic division and get 0 as the remainder which declares that it is the factor of the polynomial in which one learns in precalculus. First one retrieves  the factors of p which is the last term of the polynomial and the factors of q which is the first term of the polynomial.Then one gets the terms p/q and then use long division and then repeat the same process until it is completely factored and then use the real zeros which are the critical points and then use testing points to find where it increases and decreases. If you need further explanation please contact me.Thanks and good luck.

Answer 2

Since it cannot be factored (apparently), the best bet is to use a graphing calculator.