Learning Objectives:

__Math Tutoring on Solving Polynomial Inequality__

**Polynomial inequalities** are **inequalities** expressed with a **polynomial** on one side of the **inequality** **symbol** and **zero** on the other side. For solving **polynomial inequalities,** we need to follow the steps below:

**Step 1.** We have to manipulate the **inequality **so that we have a **polynomial** on one side of the **inequality symbol** and **zero** on the other side.

**Step 2. **Then replace the **inequality symbol** with an equal symbol and solve the equation.

**Step 3.** Next, we plot the solution from step two on a **number line.**

**Step 4.** Now we take a test value from each of the intervals, but we have to make sure they are not equal to the **endpoints** of the intervals. Then we have to plug the test values into the original **inequality. **

**Step 5.** After substitution, if the test value gives a true statement, then the interval from which it came is the solution. On the other hand, if the test value leads to a false statement, then the interval from which it came is not the solution.

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**Hook Questions**:

*1. What is a polynomial inequality? *

*2. What is a rational inequality? *

*3. How do you solve a polynomial equation?*

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