2/24 Honors Algebra Warm-up Refer to the figure. Write a polynomial to represent the area of the shaded region. A. x2ab B. C. D. x2 – ab 5Min 4-3

7-3 Polynomials: pgs. 379-380 #12-21, 22-32even, 48-50, 52, 53, 57 12. Yes; monomial 13. No 14. Yes; binomial 15. Yes; trinomial 16. Yes; trinomial 17. No 18. 1/2 bh 19. ab - 4x2 20. 1/2 xy - π r2 21. (π - 1)r2 22. 3 24. 2 26. 4 28. 2 30. 3 32. 7 48. -2x4 - 9x2y + 8x + 7y2 49. 4x3y - x2y3 + 3xy4 + y4 50. 0.25q + 0.10d + 0.05n 52. πr2h + 2/3 πr3 53. 92.15 in3 57. True; otherwise there would be no variables and the numbers could be combined.

= (7y2 + 5y2) + [2y + (–4y)] + [(– 3) + 2] Think group terms. Add Polynomials Find (7y2 + 2y – 3) + (2 – 4y + 5y2). Method 1 Horizontal = (7y2 + 5y2) + [2y + (–4y)] + [(– 3) + 2] Think group terms. = 12y2 – 2y – 1 Add like terms. Lesson 4 Ex1

Notice that terms are in descending order with like terms aligned. Add Polynomials Method 2 Vertical 7y2 + 2y – 3 (+) 5y2 – 4y + 2 Notice that terms are in descending order with like terms aligned. 12y2 – 2y – 1 Answer: 12y2 – 2y – 1 Lesson 4 Ex1

Find (3x2 + 2x – 1) + (–5x2 + 3x + 4). A. –2x2 + 5x + 3 B. 8x2 + 6x – 4 C. 2x2 + 5x + 4 D. –15x2 + 6x – 4 A B C D Lesson 4 CYP1

Think= [8y4 + (–9y4)] + [6y2 + (–2y2)] + (–5y + 7y) = –y4 + 4y2 + 2y Subtract Polynomials Find (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2). Method 1 Horizontal = 6y2 + 8y4 – 5y+ –9y4 + 7y – 2y2 Think= [8y4 + (–9y4)] + [6y2 + (–2y2)] + (–5y + 7y) = –y4 + 4y2 + 2y Lesson 4 Ex2

Subtract Polynomials Method 2 Vertical Align like terms in columns and subtract by adding the additive inverse. 8y4 + 6y2 – 5y (–) 9y4 + 2y2 – 7y 8y4 + 6y2 – 5y (+) - 9y4 – 2y2 + 7y - y4 + 4y2 + 2y Add the opposite. Answer: –y4 + 4y2 + 2y Lesson 4 Ex2

Find (3x3 + 2x2 – x4) – (x2 + 5x3– 2x4). A. 2x2 + 7x3 – 3x4 B. x4 – 2x3 + x2 C. x2 + 8x3 – 3x4 D. 3x4 + 2x3 + x2 A B C D Lesson 4 CYP2

Find an equation that models the sales of video games V(n). A. VIDEO GAMES The total amount of toy sales T (in billions of dollars) consists of two groups: sales of video games V(n) and sales of retro toys R(n). In recent years, the sales of retro toys and total sales could be modeled by the following equations, where n is the number of years since 1996. R(n) = 0.5n3 + 1.9n2 + 3n + 19 T(n) = 0.45n3 + 1.85n2 + 4.4n + 22.6 Find an equation that models the sales of video games V(n). Answer: V(n) = –0.05n3 - 0.05n2 + 1.4n + 3.6 Lesson 4 Ex3

B. What did this equation predict for the amount of video game sales is the year 1998? Answer: 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 = -0.4 – 0.2 + 2.8 + 3.6 = 5.8 billion dollars. Lesson 4 Ex3