polynomiala monomial or a sum or difference of

• polynomial—a monomial or a sum or difference of monomials • binomial—a polynomial made up of 2 monomials • trinomial—a polynomial made up of 3 monomials

Identify Polynomials State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial.

A. State whether 3 x 2 + 2 y + z is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. A. yes, monomial B. yes, binomial C. yes, trinomial D. not a polynomial A. B. C. D. A B C D

B. State whether 4 a 2 – b– 2 is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. A. yes, monomial B. yes, binomial C. yes, trinomial D. not a polynomial A. B. C. D. A B C D

C. State whether 8 r – 5 s is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. A. yes, monomial B. yes, binomial C. yes, trinomial D. not a polynomial A. B. C. D. A B C D

D. State whether 3 y 5 is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial. A. yes, monomial B. yes, binomial C. yes, trinomial D. not a polynomial A. B. C. D. A B C D

• degree of monomial—the sum of the exponents of all of its variables • degree of polynomial—the greatest degree on any monomial in the polynomial

Degree of a Polynomial A. Find the degree of 12 + 5 b + 6 bc + 8 bc 2. Step 1 Find the degree of each term. 12: degree = 0 5 b: degree = 1 6 bc: degree = 1 + 1 or 2 8 bc 2: degree = 1 + 2 or 3 Step 2 The degree of the polynomial is the greatest degree, 3. Answer: 3

Degree of a Polynomial B. Find the degree of 9 x 2 – 2 x – 4. Find the degree of each term. 9 x 2: degree = 2 4: degree = 0 2 x: degree = 1 Answer: The degree of the polynomial is 2.

A. Find the degree of 11 ab + 6 b +2 ac 2 – 7. A. 3 B. 2 C. 0 D. 1 A. B. C. D. A B C D

B. Find the degree of 3 r 2 + 5 r 2 s 2 – s 3. A. 0 B. 2 C. 4 D. 3 A. B. C. D. A B C D

• standard form of a polynomial—when a polynomial is written with the monomials arranged in decreasing degrees • leading coefficient—the coefficient of the term in a polynomial with the highest degree

Standard Form of a Polynomial A. Write 9 x 2 + 3 x 6 – 4 x in standard form. Identify the leading coefficient. Step 1 Find the degree of each term. Degree: 2 6 1 Polynomial: 9 x 2 + 3 x 6 – 4 x Step 2 Write the terms in descending order. Answer: 3 x 6 + 9 x 2 – 4 x the leading coefficient is 3.

Standard Form of a Polynomial B. Write 12 + 5 y + 6 xy + 8 xy 2 in standard form. Identify the leading coefficient. Step 1 Find the degree of each term. Degree: 1 1 2 Polynomial: 12 + 5 y + 6 xy + 8 xy 2 Step 2 Write the terms in descending order. Answer: 8 xy 2 + 6 xy + 5 y + 12 the leading coefficient is 8. 3

A. Write – 34 x + 9 x 4 + 3 x 7 – 4 x 2 in standard form. A. 3 x 7 + 9 x 4 – 4 x 2 – 34 x B. C. 9 x 4 + 3 x 7 – 4 x 2 – 34 x – 4 x 2+ 9 x 4 + 3 x 7 – 34 x D. 3 x 7 – 4 x 2 + 9 x 4– 34 x A. B. C. D. A B C D

B. Identify the leading coefficient of 5 m + 21 – 6 mn + 8 mn 3 – 72 n 3 when it is written in standard form. A. – 72 B. 8 C. – 6 D. 72 A. B. C. D. A B C D

Use a Polynomial MEDICINE From 2000 to 2006, the number N (in thousands) of patients seen by a medical facility can be modeled by the equation N = t 2 + 2. 1 t + 0. 8 where t is the number of years since 2000. How many patients were seen in 2005? Find the value of t, and substitute the value of t to find the number of patients. Since t is the number of years since 2000, t equals 2005 – 2000 or 5.

Use a Polynomial N = t 2 + 2. 1 t + 0. 8 N = 52 + 2. 1(5) + 0. 8 t = 5 N = 25 + 2. 1(5) + 0. 8 Simplify. N = 25 + 10. 5 + 0. 8 N = 36. 3 Simplify. Original equation Multiply. Answer: The number of patients in 2005 was 36. 3 thousand or 36, 300.

INSTRUMENTS From 1997 to 2005 the number P of grand pianos sold at a metropolitan store can be modeled by the equation P = 2 t 2 – 2 t + 3, where t is the number of years since 1997. How many grand pianos were sold in 2004? A. 63 pianos B. 43 pianos C. 87 pianos D. 29 pianos A. B. C. D. A B C D