Solving Polynomial Inequalities
Solving polynomials is a two step process that relies on being able to factor the polynomial, just like solving polynomial equations does.
- Find the points where the polynomial equals 0, i.e. set the polynomial part equal to 0 and solve that equation.
- Arrange the numbers from (1) in order (a number line helps for this) and pick a number between each pair of values. Test that value to see if it satisfies the original inequality or not.
The intervals whose test points satisfied the inequality are part of the solution; the intervales whose test point didn't satisfy it, aren't.
Video Lectures
Solving a polynomial inequality is a two step process: find the values that make the polynomial equal to 0 then test points between those values to see which ones satisfy the inequality and which ones don't. (lecture slides)
When solving a polynomial inequality, there are four special cases that you need to be aware. You can find each of these cases using the same method you usually use to solve this kind of inequality. It's just the final answer that can look a little unusual. (lecture slides)
