In this lesson we are going to take a look at some polynomial inequalities. When it comes to polynomial inequalities, you are going to see two techniques that you can use to handle these. One of them involves graphing, and the other one involves using a table to track down the sign. Both of these are important and since we have developed lots of graphing techniques, they are both very handy. What you need to remember is that the solution to an inequality often involves a range of values. A very common mistake that students make is using the principle of zero products. You'll see why you can't use that principle with the inequalities in the video.
Remember that the solution to an inequality often involves a range of values.
To solve an inequality involving polynomials we
Set the inequality with zero on one side
Solve the related equation, with the polynomial equal to zero
Divide the x-axis into intervals using the solutions of the equation from step 2
Use test values from each interval to see if it satisfies the inequality
Check the endpoints of each interval to see if they need to be included
Do not attempt to split up the inequality over the factors. Even though it looks like we can use the principle of zero products we can’t. This is because we have an inequality and the principle of zero products only applies to equations.
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.