Summarize how graphs can be used to find solutions to polynomial inequalities.

Step 1
1. If necessary, rewrite the inequality so that there is a zero on one side.
2. Graph the other side of the inequality.
3. Use your graphing calculator's TRACE function to the exact or approximate values of the x-intercepts.
4. Find the intervals that satisfy the inequality.
5. Write the final result as a solution interval.
Step 2
Example:
${\displaystyle x^3-4x^2+x+5\le 3}$
1. We substract 3 from both sides of the inequality:
${\displaystyle x^3-4x^2+x+2\le 0}$
2. We graph ${\displaystyle y=x^3-4x^2+x+2}$

Step 3
With the help of the graphing calculator we find the x-intercepts as ${\displaystyle x\in \{-0.562,1,3.562\}}$, rounded to three decimal digits:
Step 4
4. We note that the inequality is satisfied on the intervals ${\displaystyle (-\mathrm{\infty },-0.562]}$ and ${\displaystyle 1,3.562]}$.
5. We write the result as a solution interval:
${\displaystyle \{x\in \mathbb{R}\mid x\le -0.562\text{or}1\le x\le 3.562\}}$
or alternatively
${\displaystyle x\in (-\mathrm{\infty },-0.562]\cup [1,3.562]}$