Mastering Polynomial Inequalities and Graphs

📋 Course Outline

1. Properties of inequalities
2. Quadratic inequalities
3. Rational inequalities
4. Absolute value and square root inequalities
5. Circle and region inequalities
6. Polynomial basics
7. Polynomial operations and division
8. Remainder and factor theorems
9. Roots and coefficients
10. Multiple roots of polynomials
11. Polynomial functions
12. Graphs of polynomial functions

📖 1. Properties of inequalities

🔑 Key Concepts & Definitions

• Adding or subtracting same number : An inequality keeps the same direction when you add or subtract the same real number to both sides.
• Multiplying by positive number : An inequality keeps the same direction when you multiply both sides by a positive real number.
• Multiplying by negative number : An inequality reverses direction when both sides are multiplied by a negative real number.
• Reciprocal inequality rule : Taking reciprocals reverses inequality direction only when both sides have the same sign.
• Squaring inequalities : Squaring both sides can change the inequality direction unless you know the relative size and sign conditions.

📝 Essential Points