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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 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
Polynomials Operations Polynomial long division uses the same division algorithm as dividing real numbers.
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?
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?
The Remainder Theorem this is called synthetic division.
Synthetic Division Use synthetic division
Synthetic Division Use synthetic division
Synthetic Division Use synthetic division
The Factor Theorem kis called a zero of the function because f (k)= 0.
Factoring Polynomials –4 is a zero of the function Use synthetic division Factor more? What are the other zeros of the function?
Factoring Polynomials –5 is a zero of the function Use synthetic division Factor more? What are the other zeros of the function?
Factoring Polynomials 7 is a zero of the function Use synthetic division Factor more? What are the other zeros of the function?
Today’s Assignment • p. 356: 16, 22, 28 – 56m Change form stamp sheet
Check Assignment • p. 356: 16, 22, 28 – 56m Change form stamp sheet