5.5 Polynomials Goals: 1.To identify terms, coefficients, and factors of a term. 2.To simplify a poly by collecting like terms 3.To identify the degree of the poly

Mono__________________ Bi______________________ Tri_____________________ Poly______________________

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

To determine if an expression is a polynomial: First 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 “terms” are added, “factors” are multiplied

Is the term a polynomial? If so, say whether it is a monomial, binomial, or trinomial. No “terms” are added, “factors” are multiplied

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.

To simplify by collecting “like terms” “like terms” have the same exact variables to the same exact power. Only the coefficients may be different. 7m 2 – 2m 2 = (7 – 2)m 2 = 5m 2

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: 3m 5 – 3m 2 + m – 1 (no like terms)

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

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