5.5 Polynomials

Classic Types of Polynomials Monomial: 1 term Binomial: 2 terms Trinomial: 3 terms What are Terms??? Items separated by subtraction or addition signs

Polynomials A Polynomial is a monomial, or a sum of monomials 5x + 3 3x 2 + 2x - 5 Binomial Trinomial

Determine if an expression is a polynomial: Check that every term is a monomial If every term is a monomial then the expression is a polynomial

Is the term a polynomial? If so, say whether it is a monomial, binomial, or trinomial. y 2 + 2y Binomial, since it has two TERMS

Is the term a polynomial? If so, say whether it is a monomial, binomial, or trinomial. No

Is the term a polynomial? If so, say whether it is a monomial, binomial, or trinomial. YES, trinomial since it has 3 terms Numeric factor of a term is called the coefficient.

Identify the terms and Give the coefficient of each term.

To simplify by collecting “like terms” “like terms” have the same exact variables to the same exact power. Only the coefficients may be different.

To simplify by collecting “like terms” “like terms” have the same exact variables to the same exact power. Only the coefficients may be different. 3x 5 y 4 – 6y 4 – x 5 y 4 + 2y 4 = (3 – 1)x 5 y 4 = 2x 5 y 4 - 4y 4 y4y4 +(– 6 + 2)

Simplify by collecting like terms: 2m 4 – 4m 3 + 3m 3 – 1 2m 4 – m 3 – 1

Simplify by collecting like terms: 3x 5 y 4 – 6y 4 + m 3 – x 5 y 4 2x 5 y 4 – 6y 4 + m 3 The Degree of a term is the sum of the exponents of the variables. 9 th deg 4 th deg 3rd deg

Simplify by collecting like terms: 3x 5 y 4 – 6y 4 + m 3 – x 5 y 4 2x 5 y 4 – 6y 4 + m 3 The Degree of a term is the sum of the exponents of the variables. The Degree of a polynomial is the highest degree of any term. This is a 9 th degree polynomial.

Identify the degree of each term and the degree of the polynomial. - 63x 2 y 3 – 16xy 5 + y 4 The Degree of a term is the sum of the exponents of the variables. The Degree of a polynomial is the highest degree of any term. This is a 6 th degree polynomial. 5 th deg 6 th deg 4 th deg

Identify the degree of each term and the degree of the polynomial. 9x 6 y 5 – 7x 4 y 3 + 3xy 4 The Degree of a term is the sum of the exponents of the variables. The Degree of a polynomial is the highest degree of any term. This is a 11 th degree polynomial. 11 th deg 7 th deg 5 th deg

9x6y5 – 7x4y3 + 3xy4 Leading term is the term that has the highest degree in the poly Ex: 9x6y5 Leading coefficient is the coefficient of the leading term. Ex: 9

Assignment: Page 224 (2-52 even, 53)