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MyEducationPath.com :: Khan Academy : Trigonometry and precalculus: Polynomial and rational functions
Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions. Factoring quadratic expressions. Examples: Factoring simple quadratics. Factoring polynomials 1. Example 1: Solving a quadratic equation by factoring. Example 2: Solving a quadratic equation by factoring. Solving quadratics by factoring. Example 1: Factoring trinomials with a common factor. Factoring polynomials 2. Solving quadratics by factoring 2. Factoring Special Products. Example 1: Factoring difference of squares. Factoring difference of squares 1. Example 2: Factoring difference of squares. Factoring difference of squares 2. Factoring to produce difference of squares. Factoring difference of squares 3. Example 5: Factoring by grouping. Example 6: Factoring by grouping. Factoring polynomials by grouping. Solving Quadratic Equations by Square Roots. Solving quadratics by taking the square root. Solving Quadratic Equations by Completing the Square. Completing the square 1. Completing the square 2. How to use the Quadratic Formula. Proof of Quadratic Formula. Quadratic formula. Example: Complex roots for a quadratic. Discriminant of Quadratic Equations. Discriminant for Types of Solutions for a Quadratic. Solutions to quadratic equations. Quadratic Inequalities. Quadratic Inequalities (Visual Explanation). Terms coefficients and exponents in a polynomial. Addition and Subtraction of Polynomials. Adding and subtracting polynomials. Multiplying Polynomials. Multiplying Polynomials 3. Multiplying polynomials. Polynomial Division. Dividing polynomials 1. Dividing polynomials with remainders. Synthetic Division. Synthetic Division Example 2. Why Synthetic Division Works. Factoring Sum of Cubes. Difference of Cubes Factoring. Binomial Theorem (part 1). Binomial Theorem (part 2). Binomial Theorem (part 3). Simplifying Rational Expressions Introduction. Simplifying Rational Expressions 1. Simplifying Rational Expressions 2. Simplifying Rational Expressions 3. Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions 2. Adding and Subtracting Rational Expressions 3. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Subtracting Rational Expressions. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Multiplying and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions 1. Multiplying and Dividing Rational Expressions 2. Multiplying and Dividing Rational Expressions 3. Extraneous Solutions to Rational Equations. Rational Inequalities. Rational Inequalities 2. Asymptotes of Rational Functions. Another Rational Function Graph Example. A Third Example of Graphing a Rational Function. Partial Fraction Expansion 1. Partial Fraction Expansion 2. Partial Fraction Expansion 3. Partial fraction expansion. Factoring quadratic expressions. Examples: Factoring simple quadratics. Factoring polynomials 1. Example 1: Solving a quadratic equation by factoring. Example 2: Solving a quadratic equation by factoring. Solving quadratics by factoring. Example 1: Factoring trinomials with a common factor. Factoring polynomials 2. Solving quadratics by factoring 2. Factoring Special Products. Example 1: Factoring difference of squares. Factoring difference of squares 1. Example 2: Factoring difference of squares. Factoring difference of squares 2. Factoring to produce difference of squares. Factoring difference of squares 3. Example 5: Factoring by grouping. Example 6: Factoring by grouping. Factoring polynomials by grouping. Solving Quadratic Equations by Square Roots. Solving quadratics by taking the square root. Solving Quadratic Equations by Completing the Square. Completing the square 1. Completing the square 2. How to use the Quadratic Formula. Proof of Quadratic Formula. Quadratic formula. Example: Complex roots for a quadratic. Discriminant of Quadratic Equations. Discriminant for Types of Solutions for a Quadratic. Solutions to quadratic equations. Quadratic Inequalities. Quadratic Inequalities (Visual Explanation). Terms coefficients and exponents in a polynomial. Addition and Subtraction of Polynomials. Adding and subtracting polynomials. Multiplying Polynomials. Multiplying Polynomials 3. Multiplying polynomials. Polynomial Division. Dividing polynomials 1. Dividing polynomials with remainders. Synthetic Division. Synthetic Division Example 2. Why Synthetic Division Works. Factoring Sum of Cubes. Difference of Cubes Factoring. Binomial Theorem (part 1). Binomial Theorem (part 2). Binomial Theorem (part 3). Simplifying Rational Expressions Introduction. Simplifying Rational Expressions 1. Simplifying Rational Expressions 2. Simplifying Rational Expressions 3. Adding and Subtracting Rational Expressions. Adding and Subtracting Rational Expressions 2. Adding and Subtracting Rational Expressions 3. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Subtracting Rational Expressions. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Multiplying and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions 1. Multiplying and Dividing Rational Expressions 2. Multiplying and Dividing Rational Expressions 3. Extraneous Solutions to Rational Equations. Rational Inequalities. Rational Inequalities 2. Asymptotes of Rational Functions. Another Rational Function Graph Example. A Third Example of Graphing a Rational Function. Partial Fraction Expansion 1. Partial Fraction Expansion 2. Partial Fraction Expansion 3. Partial fraction expansion.
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