1. © Copyright by Houghton Mifflin Company. All rights reserved.1 Monomials & Polynomials  Define monomials and polynomials.  Determine the degree of a polynomial.  Describe a function using function notation.  Evaluate a polynomial for a given value of the variable

2. © Copyright by Houghton Mifflin Company. All rights reserved.2 Monomials  A monomial has: One or more variables multiplied together nonnegative, integer exponents No addition or subtraction Coefficient

3. © Copyright by Houghton Mifflin Company. All rights reserved.3 Monomials  Examples of monomials The degree of a monomial is the sum of the exponents of the variables. Degree = 1 Degree = 2+2+1=5 Degree = 0

4. © Copyright by Houghton Mifflin Company. All rights reserved.4 Polynomials  A polynomial is a sum or difference of monomials.

5. © Copyright by Houghton Mifflin Company. All rights reserved.5 Polynomials  The degree of a polynomial is the degree of the monomial with the highest degree. Degree =1 Degree = 2 Degree = 7

6. © Copyright by Houghton Mifflin Company. All rights reserved.6 Evaluating Polynomials  To evaluate a polynomial for a given value of the variable, substitute the given value for the variable.  Evaluate the polynomial for x = -3.

7. © Copyright by Houghton Mifflin Company. All rights reserved.7 Addition and Subtraction  Adding polynomials.  Subtracting polynomials.

8. © Copyright by Houghton Mifflin Company. All rights reserved.8 Adding Polynomials  Like terms of polynomials are monomials with the same variables with the same exponents. Like Terms

9. © Copyright by Houghton Mifflin Company. All rights reserved.9 Adding Polynomials  To add polynomials, combine like terms.  Add: No other like term Add 6x 2 + (-8x 2 ) Add 2x + x Add –1 + 5

10. © Copyright by Houghton Mifflin Company. All rights reserved.10 Subtracting Polynomials  To subtract polynomials, combine like terms.  Subtract: Remove parenthesis. Notice that the sign of every term in the second parenthesis changes

11. © Copyright by Houghton Mifflin Company. All rights reserved.11 Subtracting Polynomials Combine like terms: