Step 1
Step 2
\(\displaystyle{2}{x}^{{{3}}}-{5}{x}^{{{2}}}-{x}+{6}{>}{0}\)
To solve graphically we graph \(\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}-{5}{x}^{{{2}}}-{x}+{6}\). A 3rd degree polinomial can have up to 3 zeros, so make sure you can see all the important parts of the graph. We find zeros at:
\(\displaystyle{x}=-{1},{1.5},{2}\)
For the inequality, they want \(\displaystyle{f{{\left({x}\right)}}}{>}{0}\), which are the parts of the graph above the x-axis. We can see from the graph they are the intervals.
Answer:
\(\displaystyle{\left(-{1},{1.5}\right)}\cup{\left({2},\infty\right)}\)