Chapter 5 Exponents and Polynomials Section 3 Polynomials

Chapter 5 Exponents and Polynomials Section 3 Polynomials; Addition and Subtraction of Polynomials Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 1

Concept 1 Polynomial examples: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 2

Concept Degree of a Term For a polynomial in a single variable, the degree of a term is equal to the variable’s exponent. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 3

Example Degree of a Term List each term and its degree: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 2 4

Example Degree of a Term 2 Term Degree Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 5

Concept Coefficients The coefficient of a term is the numerical part of a term, including its sign. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 6

Example 3 Coefficient of a Term Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 7

Example 3 Coefficient of a Term Coefficient Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 8

Concept Degree of a Polynomial The degree of a polynomial is equal to the degree of the term that has the highest degree. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 9

Example 4 Degree of a Polynomial Degree = 6 Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 10

Concept Polynomials Monomial – A polynomial with only one term. Binomial – A polynomial with two terms. Trinomial – A polynomial with three terms. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 11

Example 5 Polynomials Monomial: Binomial: Trinomial: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 12

Concept Evaluating a Polynomial Substitute the value for the variable in the polynomial and simplify the resulting expression. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 13

Example 6 Evaluating a Polynomial Evaluate for Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 14

Concept Evaluating a Polynomial Function Substitute the value for the variable in the function and simplify the resulting expression. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 15

Example 7 Evaluating a Polynomial Function For find Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 16

Concept Adding Polynomials To add two polynomials together, combine like terms. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 17

Example 8 Adding Polynomials Add: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 18

Concept Subtracting Polynomials To subtract one polynomial from another, distribute the “-” sign and then combine like terms. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 19

Example 9 Subtracting Polynomials Subtract: Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 20

Example Evaluate the polynomial x 2 – 7 xy + 4 y 2 for x = 6 and y = – 3. x 2 – 7 xy + 4 y 2 (6)2 – 7(6)(– 3) + 4(– 3)2 10 Substitute 6 for x and – 3 for y. Perform operations involving exponents. Multiply. Add. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 21

Example 11 Add Write as a sum. Rewrite without parentheses. Combine like terms. Copyright © 2016, 2012, and 2009 Pearson Education, Inc. 22