4. Polynomial and Rational Functions

Use Long Division to Divide Polynomials

Dividing Polynomials

❖ Long Division of Polynomials ❖

Using the Remainder Theorem to Evaluate a Polynomial Video

The Remainder Theorem - Example 1

Using the remainder theorem to evaluate a polynomial

Comprehensive Graph of a Polynomial Function

The Remainder Theorem - Example 2

How to do Synthetic Division

Given f(x) = 2x^3 - 7x^2 + 9x - 3, use the Remainder Theorem to find f(- 13).

Divide a polynomial by a binomial using long division

Relate factors and zeros using the Factor Theorem

In Exercises 27–29, divide using long division. (4x^4 +6x^3 + 3x - 1) ÷ (2x^2 + 1)

Divide polynomials using long division

❖ Synthetic Division - A Shortcut for Long Division! ❖

Synthetic Division

Long Division of Polynomials - A slightly harder example

In Exercises 27–29, divide using long division. (4x^3 - 3x^2 - 2x + 1) ÷ (x + 1)

Apply the Remainder Theorem to simple division problems

Solving Higher Degree Polynomials by Synthetic Division and the Rational Roots Test

Find the roots of a polynomial using a graphing calculator

Find solutions to polynomial equations where the polynomial's remainder is zero

Divide polynomials with a missing term

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

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Use Synthetic Division to Divide Polynomials

Evaluate a Polynomial Using the Remainder Theorem

Use the Factor Theorem to Solve a Polynomial Equation

Identify Polynomial Functions

Recognize Characteristics of Graphs of Polynomial Functions

Determine End Behavior

Use Factoring to Find Zeros of Polynomial Functions

Identify Zeros and Their Multiplicities

Use the Intermediate Value Theorem

Understand the Relationship Between Degree and Turning Points

Graph Polynomial Functions

Polynomial Functions and Their Graphs

Solve Polynomial Inequalities

Solve Rational Inequalities

 Problems Modeled by Polynomial or Rational Inequalities

Polynomial and Rational Inequalities

Find the Domains of Rational Functions

Use Arrow Notation

Identify Vertical Asymptotes

Identify Horizontal Asymptotes

Use Transformations to Graph Rational Functions

Graph Rational Functions

Identify Slant Asymptotes

Solve Applied Problems Involving Rational Functions

Rational Functions and Their Graphs

Recognize Characteristics of Parabolas

Graph Parabolas

Determine a Quadratic Function's Minimum or Maximum

Problems Involving a Quadratic Function's Minimum or Maximum

Quadratic Functions

Solve Direct Variation Problems

Solve Inverse Variation Problems

Solve Combined Variation Problems

Solve Problems Involving Joint Variation

Modeling Using Variation

Use Rational Zero Theorem to Find Possible Rational Zeros

Find Zeros of a Polynomial Function

Solve Polynomial Equations

Use the Linear Factorization Theorem to Find Polynomials With Given Zeros

Use Descartes's Rule of Signs

Zeros of Polynomial Functions

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Introduction to Python

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Learn Enough JavaScript to be Dangerous: A Tutorial Introduction to Programming with JavaScript