1. Lesson 4 Menu Five-Minute Check (over Lesson 7-3) Main Ideas Targeted TEKS Example 1: Add Polynomials Example 2: Subtract Polynomials Example 3: Real-World Example

2. Lesson 4 MI/Vocab Add polynomials. Subtract polynomials.

3. Lesson 4 Ex1 Add Polynomials Find (7y 2 + 2y – 3) + (2 – 4y + 5y 2 ). Method 1 Horizontal (7y 2 + 2y – 3) + (2 – 4y + 5y 2 ) = (7y 2 + 5y 2 ) + [2y + (–4y) + [(– 3) + 2]Group like terms = 12y 2 – 2y – 1Add like terms.

4. Lesson 4 Ex1 Add Polynomials Method 2 Vertical Answer: 12y 2 – 2y – 1 7y 2 + 2y – 3 (+) 5y 2 – 4y + 2 Notice that terms are in descending order with like terms aligned. 12y 2 – 2y – 1

5. A.A B.B C.C D.D Lesson 4 CYP1 A.–2x 2 + 5x + 3 B.8x 2 + 6x – 4 C.2x 2 + 5x + 4 D.–15x 2 + 6x – 4 Find (3x 2 + 2x – 1) + (–5x 2 + 3x + 4).

6. Lesson 4 Ex2 Subtract Polynomials Find (6y 2 + 8y 4 – 5y) – (9y 4 – 7y + 2y 2 ). Method 1 Horizontal Subtract 9y 4 – 7y +2y 2 by adding its additive inverse. (6y 2 + 8y 4 – 5y) – (9y 4 – 7y + 2y 2 ) = = (6y 2 + 8y 4 – 5y) + (–9y 4 + 7y – 2y 2 ) The additive inverse of 9y 4 – 7y +2y 2 is –9y 4 + 7y – 2y 2. = [8y 4 + (–9y 4 )] + [6y 2 + (–2y 2 )] + (–5y + 7y) Group like terms. = –y 4 + 4y 2 + 2y

7. Lesson 4 Ex2 Subtract Polynomials Method 2 Vertical Align like terms in columns and subtract by adding the additive inverse. Answer: 4y 2 – y 4 + 2y or –y 4 + 4y 2 + 2y 6y 2 + 8y 4 – 5y (–) 2y 2 + 9y 4 – 7y Add the opposite. 6y 2 + 8y 4 – 5y (+) –2y 2 – 9y 4 + 7y 4y 2 – y 4 + 2y

8. Lesson 4 CYP2 1.A 2.B 3.C 4.D A.2x 2 + 7x 3 – 3x 4 B.x 4 – 2x 3 + x 2 C.x 2 + 8x 3 – 3x 4 D.3x 4 + 2x 3 + x 2 Find (3x 3 + 2x 2 – x 4 ) – (x 2 + 5x 3 – 2x 4 ).

9. Lesson 4 Ex3 A. VIDEO GAMES The total amount of toy sales T (in billions of dollars) in the United States consists of two groups: video games V and traditional toys R. In recent years, the sales of traditional toys and total sales could be modeled by the following equations, where n is the number of years since 1996. R = 0.5n 3 + 1.9n 2 – 3n – 19 T = 0.45n 3 + 1.85n 2 – 4.4n – 22.6

10. Lesson 4 Ex3 Find an equation that models the sales of video games. Subtract the polynomial for R from the polynomial for T. Answer: V = –0.05n 3 + 0.05n 2 + 1.4n + 3.6 Total 0.5n 3 + 1.9n 2 – 3n–19 – Trad. (–)0.45n 3 + 1.85n 2 –4.4n–22.6 Video –0.05n 3 + 0.05n 2 +1.4n+ 3.6 Add the opposite. 0.5n 3 +1.9n 2 – 3n– 19 (+) –0.45n 3 –1.85n 2 +4.4n+ 22.6 –0.05n 3 +0.05n 2 +1.4n+ 3.6

11. Lesson 4 Ex3 B. What did this equation predict for the amount of video game sales is the year 1998? Answer: The year 1998 is 1998 – 1996 or 2 years after the year 1996. If this trend continues, the number of video game sales in 1998 would have been –0.05(2) 3 + 0.05(2) 2 + 1.4(2) + 3.6 or 6.2 billion dollars.

12. 1.A 2.B 3.C 4.D Lesson 4 CYP3 A.50x 2 – 50x + 500 B.–50x 2 – 50x + 500 C.250x 2 + 950x + 500 D.50x 2 + 950x + 100 A. BUSINESS The profit a business makes is found by subtracting the cost to produce an item C from the amount earned in sales S. The cost to produce and the sales amount could be modeled by the following equations, where x is the number of items produced. C = 100x 2 + 500x – 300 S = 150x 2 + 450x + 200 Find an equation that models the profit.

13. 1.A 2.B 3.C 4.D Lesson 4 CYP3 A.$500 B.$30 C.$254,000 D.$44,000 B. What does this equation predict the profit would be if 30 items were produced and sold?