Identifying Polynomials 12152021 Identifying Polynomials 1 Monomial a

Identifying Polynomials 12/15/2021 Identifying Polynomials 1

• Monomial – a number, a variable, or the product of a number and one or more variables with whole number exponents Ex. 8 -2 x 3 x 2 y 1/2 x 2 • Degree of a monomial – the sum of the exponents of the variables in the monomial Ex. 8 is the 0 degree -2 x is the 1 degree 3 x 2 y is the 3 degree 1/2 x 2 is the 2 degree 12/15/2021 10. 1 Adding and Subtracting Polynomials 2

Ex. 1. State the degree of the monomial. a. -5 x 4 4 degree b. 1/2 b 3 3 degree c. 12 0 degree d. 6 x 3 3 degree 12/15/2021 e. 4 p 1 degree f. -10 0 degree g. -3 a 5 5 degree 10. 1 Adding and Subtracting Polynomials 3

• Polynomial – a monomial or a sum of monomials Ex. 4 x 3 x 3 -8 7 x 2 -4 x+6 • Binomial – a polynomial of 2 terms • Trinomial – a polynomial of 3 terms • Standard Form – terms are written in decreasing order • Degree of a Polynomial – the degree of the term with the largest degree • Constant – a polynomial of 0 degree • Linear – a polynomial of 1 degree • Quadratic – a polynomial of 2 degree • Cubic – a polynomial of 3 degree 12/15/2021 10. 1 Adding and Subtracting Polynomials 4

Ex. 2. Identify the Polynomial Degree • • 0 1 2 3 6 3 x+1 x 2 -x-5 4 x 3 -8 x 12/15/2021 Identified by Degree Constant Linear Quadratic Cubic 10. 1 Adding and Subtracting Polynomials Identified by Number of Terms Monomial Binomial Trinomial Binomial 5

Ex. 3. Identify the Polynomial Degree a. b. c. d. e. f. g. 1 1 2 3 0 2 1 8 x 10 x-5 x 2 -4 x+4 -24 -x 3 -5 -6 x 2 -6 1/2 x 12/15/2021 Identified by Degree Linear Quadratic Cubic Constant Quadratic Linear 10. 1 Adding and Subtracting Polynomials Identified by Number of Terms Monomial Binomial Trinomial Binomial Monomial 6