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MATH 1111 - College Algebra: 4.1 Finding Zeros of Polynomial Functions

4.1 Finding Zeros of Polynomial Functions

At the end of this section students will be able to:

  • Use synthetic division to divide polynomials
  • Evaluate polynomials using the Remainder Theorem
  • Use the Factor Theorem to factor polynomials
  • Use the Rational Zeros Theorem in finding possible zeros of a polynomial with integers coefficients
  • Determine all zeros of a polynomial function with real coefficients

Required Reading

3.2 The Factor Theorem and the Remainder Theorem

Stitz-Zeager College Algebra - pages 257-264

 

3.3 Real Zeros of Polynomials

Stitz-Zeager College Algebra - pages 269-270

Practice Exercises

The Factor Theorem and the Remainder Theorem

Stitz-Zeager College Algebra - pages 265-266

Answers to practice exercises can be found on pages 267-268.

Real Zeros of Polynomials

Stitz-Zeager College Algebra - pages 280

Answers to practice exercises can be found on pages 283.

Supplemental Resources

Synthetic Division and the Remainder and Factor Theorems (tutorial): West Texas A&M University Virtual Math Lab (College Algebra Tutorial 37)

Zeros of Polynomial Functions (tutorial): West Texas A&M University Virtual Math Lab (College Algebra Tutorial 38)

 

Synthetic Division:

Evaluating Polynomials Using the Remainder Theorem:

 

Finding All Zeros of A Polynomial Function:

Example 1

 

Example 2

 

Example 3