Chapter 10 Polynomials Tab 1 Identifying Polynomials Definition

Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Definition Polynomials : Is a monomial or a sum of monomials The prefix poly- means more than one, the suffix –nomial mean name but in math it means terms. Therefore, Polynomial means more than one term. Examples of Polynomials: * Terms are separated by a + or - sign. 2 12 x³y 8 x² + 4 x – 3 x² - 9

Identifying Polynomials are identified in two ways by the number of terms and by degree.

Identifying Polynomials by Terms Monomial: Mon means one, a polynomial with one term. Examples of Monomials: -4 x 5 6 x²y³

Identifying Polynomials by Terms * Terms are separated by a + or - sign. • Binomial: Bi means two, a polynomial with two terms. Examples of Binomials: -4 x + 3 x³- 225 6 x²y³ - x

Identifying Polynomials by Terms * Terms are separated by a + or - sign. Trinomial: Tri means three, a polynomial with three terms. Examples of Trinomials: 8 x² + 4 x – 3 x²y³ + xy² – y 64 y³ + y² – 2 * More than 3 terms is called a polynomial*

Identifying Polynomials by Degree of the Polynomial is determined by the largest exponent of the variable. Examples: 5 x³ + 4 x² -6 x² + 4 3 x + 1 2 has a degree of 3 has a degree of 2 has a degree of 1 has a degree of 0 Cubic Quadratic Linear Constant * More than a degree of 3 , just write the number. *

Let’s Put IT All Together Polynomial 6 3 x + 1 -x²+2 x-5 4 x³ - 8 x 5 x³+4 x²-6 x+14 Degree Identify by Terms

Let’s Put IT All Together Polynomial Degree 6 0 3 x + 1 -x²+2 x-5 4 x³ - 8 x 5 x³+4 x²-6 x+14 Identify by Degree Identify by Terms

Let’s Put IT All Together Polynomial Degree 6 0 3 x + 1 -x²+2 x-5 4 x³ - 8 x 5 x³+4 x²-6 x+14 Identify by Degree Constant Identify by Terms

Let’s Put IT All Together Polynomial Degree 6 0 3 x + 1 -x²+2 x-5 4 x³ - 8 x 5 x³+4 x²-6 x+14 Identify by Degree Constant Identify by Terms Monomial

Let’s Put IT All Together Polynomial Degree 6 0 3 x + 1 1 -x²+2 x-5 4 x³ - 8 x 5 x³+4 x²-6 x+14 Identify by Degree Constant Identify by Terms Monomial

Let’s Put IT All Together Polynomial Degree 6 0 Identify by Degree Constant 3 x + 1 1 Linear -x²+2 x-5 4 x³ - 8 x 5 x³+4 x²-6 x+14 Identify by Terms Monomial

Let’s Put IT All Together Polynomial Degree 6 3 x + 1 -x²+2 x-5 4 x³ - 8 x 5 x³+4 x²-6 x+14 0 Identify by Degree Constant Identify by Terms Monomial 1 Linear Binomial

Let’s Put IT All Together Polynomial Degree 0 Identify by Degree Constant Identify by Terms Monomial 6 3 x + 1 1 Linear Binomial -x²+2 x-5 2 4 x³ - 8 x 5 x³+4 x²-6 x+14

Let’s Put IT All Together Polynomial Degree 0 Identify by Degree Constant Identify by Terms Monomial 6 3 x + 1 1 Linear Binomial -x²+2 x-5 2 Quadratic 4 x³ - 8 x 5 x³+4 x²-6 x+14

Let’s Put IT All Together Polynomial Degree 0 Identify by Degree Constant Identify by Terms Monomial 6 3 x + 1 1 Linear Binomial -x²+2 x-5 2 Quadratic Trinomial 4 x³ - 8 x 5 x³+4 x²-6 x+14

Let’s Put IT All Together Polynomial Degree 0 Identify by Degree Constant Identify by Terms Monomial 6 3 x + 1 1 Linear Binomial -x²+2 x-5 2 Quadratic Trinomial 4 x³ - 8 x 3 5 x³+4 x²-6 x+14

Let’s Put IT All Together Polynomial Degree 0 Identify by Degree Constant Identify by Terms Monomial 6 3 x + 1 1 Linear Binomial -x²+2 x-5 2 Quadratic Trinomial 4 x³ - 8 x 3 Cubic 5 x³+4 x²-6 x+14

Let’s Put IT All Together Polynomial Degree 0 Identify by Degree Constant Identify by Terms Monomial 6 3 x + 1 1 Linear Binomial -x²+2 x-5 2 Quadratic Trinomial 4 x³ - 8 x 3 Cubic Binomial 5 x³+4 x²-6 x+14

Let’s Put IT All Together Polynomial Degree 0 Identify by Degree Constant Identify by Terms Monomial 6 3 x + 1 1 Linear Binomial -x²+2 x-5 2 Quadratic Trinomial 4 x³ - 8 x 3 Cubic Binomial 5 x³+4 x²-6 x+14 3

Let’s Put IT All Together Polynomial Degree 0 Identify by Degree Constant Identify by Terms Monomial 6 3 x + 1 1 Linear Binomial -x²+2 x-5 2 Quadratic Trinomial 4 x³ - 8 x 3 Cubic Binomial 5 x³+4 x²-6 x+14 3 Cubic

Let’s Put IT All Together Polynomial Degree 0 Identify by Degree Constant Identify by Terms Monomial 6 3 x + 1 1 Linear Binomial -x²+2 x-5 2 Quadratic Trinomial 4 x³ - 8 x 3 Cubic Binomial 5 x³+4 x²-6 x+14 3 Cubic Polynomial