Wednesday, September 18, 2024

# Holt Algebra 2 Lesson 6 2 Multiplying Polynomials

## Presentation On Theme: 7

Algebra 2 6 3 Lesson Part 1 Adding, Subtracting, and Multiplying Polynomials

1 7-5PolynomialsWarm UpLesson PresentationLesson QuizHolt Algebra 1

2 A polynomial is a monomial or a sum or difference of monomials.The degree of a polynomial is the degree of the term with the greatest degree.

3 Example 2: Finding the Degree of a PolynomialFind the degree of each polynomial.A. 11×7 + 3x311x7: degree 7 3×3: degree 3Find the degree of each term.The degree of the polynomial is the greatest degree, 7.B.:degree 3:degree 45: degree 0Find the degree of each term.The degree of the polynomial is the greatest degree, 4.

4 Check It Out! Example 2Find the degree of each polynomial.a. 5x 65x: degree 16: degree 0Find the degree of each term.The degree of the polynomial is the greatest degree, 1.b. x3y2 + x2y3 x4 + 2Find the degree of each term.x3y2: degree 5x2y3: degree 5×4: degree 42: degree 0The degree of the polynomial is the greatest degree, 5.

5 The terms of a polynomial may be written in any orderThe terms of a polynomial may be written in any order. However, polynomials that contain only one variable are usually written in standard form.The standard form of a polynomial that contains one variable is written with the terms in order from greatest degree to least degree. When written in standard form, the coefficient of the first term is called the leading coefficient.

12 Like terms are constants or terms with the same variable raised to the same power. To review combining like terms, see lesson 1-7.Remember!

## Multiplying Polynomials Lesson Quiz Lesson Presentation

• Slides: 8

6 -2 Multiplying Polynomials Lesson Quiz Lesson Presentation Holt Algebra 22

6 -2 Multiplying Polynomials Lesson Quiz Find each product. 1. 5 jk 2. 2 a 2 + 7 a 15 Holt Algebra 2 5 jk 2 10 j 2 k

6 -2 Multiplying Polynomials Objectives Multiply polynomials. Holt Algebra 2

6 -2 Multiplying Polynomials To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents. Holt Algebra 2

6 -2 Multiplying Polynomials Exponent Rules When you multiply like bases, you add the exponents and the base stays the same . When you divide like bases, you subtract the exponents and the base stays the same. Power raised to a power, you multiply the powers and the base stays the same. Zero exponent, the answer is one and the base goes away. Negative exponent, send the base to the other side, and the exponent becomes positive. Holt Algebra 2

6 -2 Multiplying Polynomials Check It Out! Example 2 b Find the product. Multiply each term of one polynomial by each term of the other. Use a table to organize the products. x 2 4 x 1 The top left corner is the first 4 3 2 x 4 x x term in the product. Combine terms along diagonals to get 2 5 x 5 x 3 20 x 5 x the middle terms. The bottom right corner is the last term in the product. x 4 + + + x 4 + x 3 19 x 2 + 5 x Holt Algebra 2

6 -2 Multiplying Polynomials Assignment ALL Odd numbers Starting with 1. Need to see 1, 3, 5 before you leave class today. Due Wed/Thurs Quiz Tomorrow Holt Algebra 2

## Multiplying Polynomials Warm Up Lesson Presentation

• Slides: 11

6 -2 Multiplying Polynomials Warm Up Lesson Presentation Lesson Quiz Holt Algebra 22

6 -2 Multiplying Polynomials Warm Up Multiply. 1. x x 4 2. 3 x 2 3 x 7 3. 2 10 x 3 4. x 6 x 3 5. xy 7 x 3 y 6. 3 y 2 9 y 3 Holt Algebra 2

6 -2 Multiplying Polynomials Objectives Multiply polynomials. Holt Algebra 2

6 -2 Multiplying Polynomials To multiply a polynomial by a monomial, use the Distributive Property and the Properties of Exponents. Holt Algebra 2

6 -2 Multiplying Polynomials Exponent Rules When you multiply like bases, you add the exponents and the base stays the same . When you divide like bases, you subtract the exponents and the base stays the same. Power raised to a power, you multiply the powers and the base stays the same. Zero exponent, the answer is one and the base goes away. Negative exponent, send the base to the other side, and the exponent becomes positive. Holt Algebra 2

6 -2 Multiplying Polynomials Example 1: Multiplying a Monomial and a Polynomial Find each product. A. 4 x y -3 x 4 x 4 xy 12 x 2 Distribute. Multiply. 4 xy 12 x 2 B. fg f 4 2 f 3 g 3 f 2 g 2 fg f 5 g 2 f 4 g 2 3 f 3 g 3 f 5 g + 2 f 4 g 2 3 f 3 g 3 Holt Algebra 2 Distribute. Multiply.

6 -2 Multiplying Polynomials Assignment Multiples of 3 Page 1 5 Page 2 Due Tuesday Quiz Tomorrow Holt Algebra 2

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## Presentation On Theme: Holt Mcdougal Algebra 1 7

1 Holt McDougal Algebra 1 7-8 Multiplying Polynomials 7-8 Multiplying Polynomials Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Algebra 1

2 7-8 Multiplying Polynomials Warm Up Evaluate. 1. 3 2 3. 10 2 Simplify. 4. 2 3 2 4 6. 2 9 16 100 2727 2. 242. 24 5. y 5 y 4 5656 7. 4 8. 4 4 x + 28 y9y9 x8x8

3 Holt McDougal Algebra 1 7-8 Multiplying Polynomials Multiply polynomials. Objective

4 Holt McDougal Algebra 1 7-8 Multiplying Polynomials To multiply monomials and polynomials, you will use some of the properties of exponents that you learned earlier in this chapter.

5 Holt McDougal Algebra 1 7-8 Multiplying Polynomials Multiply. Example 1: Multiplying Monomials A. 18 y 8 Group factors with like bases together. B. 27 m 3 n 3 Multiply. Group factors with like bases together. Multiply.

6 Holt McDougal Algebra 1 7-8 Multiplying Polynomials When multiplying powers with the same base, keep the base and add the exponents. x 2 x 3 = x 2+3 = x 5 Remember!

7 Holt McDougal Algebra 1 7-8 Multiplying Polynomials Check It Out! Example 1 Multiply. a. 18 x 5 Group factors with like bases together. Multiply. Group factors with like bases together. Multiply. b. 10 r 2 t 4

9 Holt McDougal Algebra 1 7-8 Multiplying Polynomials To multiply a polynomial by a monomial, use the Distributive Property.

21 Holt McDougal Algebra 1 7-8 Multiplying Polynomials In the expression 2, the base is . 2 = Helpful Hint