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Chapter 6 Lesson 5: The Remainder & Factor Theorem

Chapter 6 Lesson 5: The Remainder & Factor Theorem. State Standards. Lesson Goals. 3: Add, subtract, multiply and divide (including long division) polynomials. 4: Factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.

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Chapter 6 Lesson 5: The Remainder & Factor Theorem

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  1. Chapter 6 Lesson 5:The Remainder & Factor Theorem State Standards Lesson Goals 3: Add, subtract, multiply and divide (including long division) polynomials. 4: Factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. • Divide polynomials and relate the results to the remainder theorem and the factor theorem ESLRs: Becoming Competent Learners and Complex Thinkers

  2. Polynomials Operations Polynomial long division uses the same division algorithm as dividing real numbers.

  3. Long Division with Polynomials

  4. Long Division with Polynomials

  5. Long Division with Polynomials Use synthetic substitution to evaluate the dividend when x = –2. How does the answer when evaluating compare to the remainder when dividing? How do the other numbers in the last row of synthetic substitution compare to the answer when dividing?

  6. Long Division with Polynomials

  7. Long Division with Polynomials Use synthetic substitution to evaluate the dividend when x = –6. How does the answer when evaluating compare to the remainder when dividing? How do the other numbers in the last row of synthetic substitution compare to the answer when dividing?

  8. The Remainder Theorem this is called synthetic division.

  9. Synthetic Division Use synthetic division

  10. Synthetic Division Use synthetic division

  11. Synthetic Division Use synthetic division

  12. The Factor Theorem kis called a zero of the function because f (k)= 0.

  13. Factoring Polynomials –4 is a zero of the function Use synthetic division Factor more? What are the other zeros of the function?

  14. Factoring Polynomials –5 is a zero of the function Use synthetic division Factor more? What are the other zeros of the function?

  15. Factoring Polynomials 7 is a zero of the function Use synthetic division Factor more? What are the other zeros of the function?

  16. You Try

  17. You Try

  18. Today’s Assignment • p. 356: 16, 22, 28 – 56m Change form stamp sheet

  19. Check Assignment • p. 356: 16, 22, 28 – 56m Change form stamp sheet

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