Quick: What do you get when you cross a polynomial or rational function? (dramatic pause) A rational or polynomial inequality! (Of course it's not funny. This is math.)
As with all inequalities, these ones will result in a "shading one side of the number line" situation, or perhaps an "interval notation" situation, or both. No worries, though! The first video below will be a reprise of a video about quadratic inequalities from back in Algebra, when we only saw exponents of x2. The videos after that will break into the bigtime of higher-power polynomial inequalities. Rational inequalities are very similar, with slight differences, so that's why they're in this chapter with the others. Now sit back, and relax, and see how "test points" are your new best friend!
This video is all about what to do when your quadratic "equation" suddenly has a "<" or ">" instead of an equals sign. Not surprisingly, to solve "quadratic inequalities" we'll use a fun combination of the "quadratic" methods from this chapter (factoring mostly) and solving inequalities stuff from the previous chapter.
Not so different from the quadratic inequalities of the previous video, just more spots on number line! Plus, since there's more factors to play with (as your egghead teacher might say), they can pull some fun (their word) and/or mean tricks (mine) with exponents and repeated roots.
What happens when you put two polynomials above each other in an inequality? Believe it or not, it's not that much worse than if there was no fraction, just gotta be careful with open dots! (For a refresher on finding common denominators when x's and x2's are involved, check out my solving rational equations video.)
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)