Currently, we are learning how to solve inequalities of degrees greater than 2 such as $x^3+9x^2+26x+24 < 0$.
Our teacher told us to graph and find the intervals to solve for $x$ but is there an efficient method to find the $x$'s rather than graphing them? Our teacher also told us to find each case, but that is also inefficient.
What is the best method to find the $x$'s of any inequality greater than degree 2?
NOTE: We aren't going to be finding inequalities for degrees higher than 4. Therefore, if there does exist such a method that works more efficiently with relatively low degrees, then that is fine also.