1 Identify monomials 2 Identify the coefficient and

* 1. Identify monomials. 2. Identify the coefficient and degree of a monomial. 3. Classify polynomials. 4. Identify the degree of a polynomial. 5. Evaluate polynomials. 6. Write polynomials in descending order of degree. 7. Combine like terms.

* Identify monomials. *

a number x, y Monomial: An expression that is a constant, a variable, or a product of a constant and variable(s) that are raised to whole number powers. Multiply a number and a variable Exponent can’t be negative! Exponent can’t have fractions!

Is the given expression a monomial: Yes When an equation in one variable is solved the answer is a point on a line. No No

* Identify the coefficient and degree of a monomial. * Copyright © 2011 Pearson Education, Inc.

Coefficient of a monomial: The numerical factor in a monomial. Degree of a monomial: The sum of the exponents of all variables in a monomial. Copyright © 2011 Pearson Education, Inc.

Identify the coefficient and degree of each monomial: C: 8 D: 2 C: -1 D: 1 C: one 18 When an equation in variable is solved the answer is a point on a line C: . D: 0 C: 23 = 8 D: 5 -6. 7 D: 3 C: 16 D: 0

* Classify polynomials. Clear Target 4 Identify the degree of a polynomial. * Copyright © 2011 Pearson Education, Inc.

Polynomial: A monomial or an expression that can be written as a sum of monomials. Examples: 4 x, 4 x + 8, 2 x 2 - 5 xy + 8 y Polynomial in one variable: A polynomial in which every variable term has the same variable. Example: x 2 – 5 x + 2 Copyright © 2011 Pearson Education, Inc.

Binomial: A polynomial containing two terms. Trinomial: A polynomial containing three terms. Degree of a polynomial: The greatest degree of any of the terms in the polynomial. Copyright © 2011 Pearson Education, Inc.

Identify the type of polynomial and the degree: Binomial D: 2 Monomial D: 3 When an equation in one variable is solved the answer is a point on a line. Trinomial D: 3 Not a polynomial Polynomial D: 3 Polynomial D: 4

* Evaluate polynomials. * Copyright © 2011 Pearson Education, Inc.

Evaluate each of the following: -2(-1)2(4) = -8 (-4)2 – (-4) – 3 = 16 + 4 – 3 = 17 - (-1)2 (2) = - (1)(2) = -2

Combine like terms and write the resulting polynomial in descending order of degree.

*The next six problems will be completed in your notes to summarize todays lesson. *

Classify the expression a) Monomial b) Binomial c) Trinomial d) None of these Copyright © 2011 Pearson Education, Inc. 5. 2 Slide 5 - 16

Classify the expression a) Monomial b) Binomial c) Trinomial d) None of these Copyright © 2011 Pearson Education, Inc. 5. 2 Slide 5 - 17

Evaluate when x = – 3. a) – 118 b) – 10 c) 10 d) 134 Copyright © 2011 Pearson Education, Inc. 5. 2 Slide 5 - 18

Evaluate when x = – 3. a) – 118 b) – 10 c) 10 d) 134 Copyright © 2011 Pearson Education, Inc. 5. 2 Slide 5 - 19

Identify the degree of the polynomial. a) 3 b) 5 c) 6 d) 7 Copyright © 2011 Pearson Education, Inc. 5. 2 Slide 5 - 20

Identify the degree of the polynomial. a) 3 b) 5 c) 6 d) 7 Copyright © 2011 Pearson Education, Inc. 5. 2 Slide 5 - 21