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.

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

Objective 2 Identify the coefficient and degree of a monomial.

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.

Identify the coefficient and degree of each monomial: x0 C: -6.7 D: 3 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

Objective 3 Classify polynomials. Objective 4 Identify the degree of a polynomial.

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

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.

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

Objective 5 Evaluate polynomials.

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

Objective 6 Write polynomials in descending order of degree. Objective 7 Combine like terms.

Writing a Polynomial in Descending Order of Degree Place the highest degree term first, then the next highest degree, and so on.

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