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Mastering Polynomial Division: Techniques and Theorems

This guide provides an overview of polynomial division methods, including long division and synthetic division. Scholars will learn how to apply the Remainder and Factor Theorems to identify factors and zeros of polynomials. Key points from recent lessons will help reinforce understanding. Additionally, quizzes and reflections on the topic will ensure comprehension. By mastering these techniques, students will confidently factor polynomials and solve related problems. Join us in exploring the fundamentals of polynomial division that lay the groundwork for advanced mathematics.

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Mastering Polynomial Division: Techniques and Theorems

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  1. Do Now • Solve. Check your answers for extraneous solutions:

  2. Objectives • 15.October.2012 • Scholars will be able to… • Divide polynomials using long division and synthetic division. • Use the Remainder and Factor Theorems.

  3. Wait • Write down two key points from Friday and one question.

  4. Quiz Reflections

  5. Dividing Polynomials • Graph . • Where does this have a zero? • We know that this has a zero at . • Therefore divides the polynomial and the result will be some other polynomial . • Here we can factor and figure out what is quickly.

  6. Old School Long Division Break

  7. Dividing with Long Division • Factor if is a factor:

  8. Dividing with Long Division • Factor if there is a zero at :

  9. Dividing with Long Division • Factor if is a factor:

  10. Divide • Is the quotient a polynomial? • Is a factor of ?

  11. Divide

  12. Divide

  13. Divide

  14. Divide

  15. Divide

  16. Synthetically Divide

  17. Synthetically Divide

  18. Synthetically Divide

  19. Remainder Theorem • If is a polynomial divided by , the remainder is . • A polynomial has a factor of iff.

  20. Example • Is a factor of ? • Is a factor of ?

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