2. 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?

3. 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

4. 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

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

6. 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

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

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

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

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

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

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

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

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

15. Example 4 Major League Baseball teams are divided into two leagues. During the period 2005-2011, the attendance N and A (in thousands) at National and American League baseball games, respectively, can be modeled by N:-488t 2 + 5430t + 24,700 A:-318t 2 + 3040t + 25,600 where t is the number of years since 2005. (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.

16. Example 4 N:-488t 2 + 5430t + 24,700 A:-318t 2 + 3040t + 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 2005. Write a polynomial expression that represents the difference in attendance between the two leagues.