1. 8.5 Adding and Subtracting Polynomials

2. Warm up… From 1996 to 1999, the amount of sales (in billions of dollars) of video games V and traditional toys R in the US can be modeled by the following equations where t is the number of years since 1996. Can you write an equation for the total toys (T) sold?

3. Add Polynomials To add polynomials, group the LIKE TERMS LIKE TERMS are variables that have the SAME LETTER and the SAME POWER.

4. Add polynomials – METHOD 1 (3x 2 - 4x + 8) + (2x - 7x 2 - 5) =(3x 2 - 7x 2 ) + ( -4x + 2x) + (+8 - 5) =-4x 2 - 2x + 3

5. Add polynomials – METHOD 2 (3x 2 -4x+8) + (2x-7x 2 -5) -4x 2 - 2x + 3 3x 2 - 4x + 8 (+) -7x 2 + 2x - 5

6. Subtract polynomials – METHOD 1 (3x 2 + 13x 3 + 5x) - (7x + 4x 3 ) =(3x 2 + 13x 3 + 5x) + (-7x - 4x 3 ) = (13x 3 - 4x 3 ) + 3x 2 + (5x -7x) = 9x 3 + 3x 2 - 2x

7. Subtract polynomials – METHOD 2 (3x 2 + 13x 3 + 5x) - (7x + 4x 3 ) =(3x 2 + 13x 3 + 5x) + (-7x - 4x 3 ) 13x 3 + 3x 2 + 5x (+) - 4x 3 - 7x 9x 3 + 3x 2 - 2x

8. Subtract Polynomials The total number of public school teachers consists of two groups, elementary and secondary. From 1985 through 1988, the number (in thousands) of secondary teachers and the total teachers could be modeled by the following equations, where n is the number of years since 1985.

9. Subtract Polynomials Find an equation that models the number of elementary teachers, E, for the same time period.

10. Subtract Polynomials Predict the number of elementary teachers in the year 2010.

11. Warm up… From 1996 to 1999, the amount of sales (in billions of dollars) of video games and traditional toys can be modeled by the following equations where t is the number of years since 1996. Can you write an equation for the total toys (T) sold?

12. Warm up…

13. Homework P441:13-31odd Notes 8.5