Understanding the Basics
Polynomial inequalities involve expressions with polynomials on one or both sides of an inequality sign. The typical inequality signs are <, >, ≤, and ≥. For example, \(x^2 + 3x + 2 < 0\).
Steps to Solve Polynomial Inequalities
- Factor the Polynomial: Find the roots by factoring.
- Determine Intervals: Use these roots to break the number line into intervals.
- Test Intervals: Determine where the expression is positive or negative.
- Write the Solution Set: Choose the intervals where the inequality holds true.
Practice Problem
Solve the inequality: \(2x^3 - 3x^2 - 5x > 0\).