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Multiplying and Dividing Polynomials

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1 Multiplying and Dividing Polynomials
Algebra II with Trigonometry Ms. Lee

2 Essential Question Essential Vocabulary
How do you multiply and divide polynomials? How do you know if a polynomial will have a remainder? Essential Vocabulary Like Terms Synthetic Division Remainder Theorem

3 Multiplying Polynomials
Multiply each term of one polynomial by each term in the other polynomial. Remember when multiplying variables with exponents, add the exponents. Example: 𝑥 4 ∙ 𝑥 3 = 𝑥 7 MULTIPLICATION Examples

4 Dividing Polynomials DIVISION
Long division of polynomials is like long division of numbers. If a binomial goes into polynomial evenly (remainder of 0), then the binomial is a factor of the polynomial. DIVISION

5 Synthetic Division Synthetic division is a simplified method for dividing polynomials and uses only the coefficients of the polynomial. We can use synthetic division to find all zeros/factors of a polynomial. Examples

6 Remainder Theorem If a polynomial P(x) of degree n is divided by (x – a), then the remainder is P(a). In other words, when you plug a value into the polynomial, the solution is the remainder of the polynomial. How is this theorem helpful for us? Examples

7 Homework Homework 6.2


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