Essential Questions  What are the similarities and differences between monomials and polynomials?  How are polynomials added and subtracted, and how does this relate to combining like terms?  How are polynomials used in real world applications?

Monomial  A number, a variable, or the product of a number and one or more variables with whole number exponents  Examples: 10, x, 3x, ½ ab 2  Non-examples: 5 + x, 2/n, x -1, 10 x

Polynomial  A monomial or a sum of monomials, each called the terms of the polynomial  Binomial: a polynomial with 2 terms  Trinomial: a polynomial with 3 terms

Descending Order  Most polynomials are written so that the exponents of the terms decrease from left to right, which is called descending order.

Example 1 Tell whether the expression is a polynomial. If it is, classify it by the number of terms. Otherwise, tell why it is not a polynomial. ExpressionPolynomialClassify/Explain (A)9 (B)2x 2 + x – 5 (C)6n 4 – 3 n (D)n -2 – 3 (E)7b 3 + 4bc 2 (F)3x 4 – 2x 3 + 6x 2 – 5x + 1

Adding Polynomials  To add polynomials, add like terms either horizontally or vertically.

Example 2: Find the sum (A) (2x 3 – 5x 2 + x) + (2x 2 + x 3 – 1)

Example 2: Find the sum (B) (3x 2 + x – 6) + (x 2 + 4x + 10)

Example 2: Find the sum (C) Add vertically: (4x 3 + 2x 2 – 4) + (x 3 – 3x 2 + x)

Subtracting Polynomials  To subtract a polynomial, add the opposite of the second polynomial.  You may also think of it as “distributing -1.”

Example 3: Find the difference (A) (4n 2 + 5) – (-2n 2 + 2n – 4)

Example 3: Find the difference (B) (5y 2 + 2y – 4) – (3y 2 – 4y + 1)

Example 3: Find the difference (C) Subtract vertically: (5y 2 – 2y – 8) – (-y 2 + 4y – 3)

Example 4 Major League Baseball teams are divided into two leagues. During the period , the attendance N and A (in thousands) at National and American League baseball games, respectively, can be modeled by N:-488t t + 24,700 A:-318t t + 25,600 where t is the number of years since (A)Find the polynomial expression that represents the total attendance for all Major League Baseball games. (B)Find how many people attended games in 2011.

Example 4 N:-488t t + 24,700 A:-318t t + 25,600 (C) Predict the total attendance in 2014, assuming the trend continues. What conclusion can be drawn? (D) The American League attendance is higher than the National League in Write a polynomial expression that represents the difference in attendance between the two leagues.