Introduction to Polynomials

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Presentation transcript:

Introduction to Polynomials 5.2 Introduction to Polynomials 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. Copyright © 2011 Pearson Education, Inc.

Objective 1 Identify monomials.

x, y a number 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 Yes When an equation in one variable is solved the answer is a point on a line. No No

Copyright © 2011 Pearson Education, Inc. Objective 2 Identify the coefficient and degree of a monomial. Copyright © 2011 Pearson Education, Inc.

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: When an equation in one variable is solved the answer is a point on a line. C: 16 D: 0 C: 23 = 8 D: 5

Copyright © 2011 Pearson Education, Inc. Objective 3 Classify polynomials. Objective 4 Identify the degree of a polynomial. Copyright © 2011 Pearson Education, Inc.

Copyright © 2011 Pearson Education, Inc. Polynomial: A monomial or an expression that can be written as a sum of monomials. Examples: 4x, 4x + 8, 2x2 - 5xy + 8y Polynomial in one variable: A polynomial in which every variable term has the same variable. Example: x2 – 5x + 2 Copyright © 2011 Pearson Education, Inc.

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 Polynomial D: 3 Polynomial D: 4 Not a polynomial

Copyright © 2011 Pearson Education, Inc. Objective 5 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

Copyright © 2011 Pearson Education, Inc. Objective 6 Write polynomials in descending order of degree. Objective 7 Combine like terms. Copyright © 2011 Pearson Education, Inc.

Copyright © 2011 Pearson Education, Inc. Writing a Polynomial in Descending Order of Degree Place the highest degree term first, then the next highest degree, and so on. Copyright © 2011 Pearson Education, Inc.

Write the polynomial in descending order.

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

Copyright © 2011 Pearson Education, Inc. Classify the expression a) Monomial b) Binomial c) Trinomial d) None of these Copyright © 2011 Pearson Education, Inc. 5.2

Copyright © 2011 Pearson Education, Inc. Classify the expression a) Monomial b) Binomial c) Trinomial d) None of these Copyright © 2011 Pearson Education, Inc. 5.2

Copyright © 2011 Pearson Education, Inc. Evaluate when x = –3. a) –118 b) –10 c) 10 d) 134 Copyright © 2011 Pearson Education, Inc. 5.2

Copyright © 2011 Pearson Education, Inc. Evaluate when x = –3. a) –118 b) –10 c) 10 d) 134 Copyright © 2011 Pearson Education, Inc. 5.2

Copyright © 2011 Pearson Education, Inc. Identify the degree of the polynomial. a) 3 b) 5 c) 6 d) 7 Copyright © 2011 Pearson Education, Inc. 5.2

Copyright © 2011 Pearson Education, Inc. Identify the degree of the polynomial. a) 3 b) 5 c) 6 d) 7 Copyright © 2011 Pearson Education, Inc. 5.2