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.

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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

Lesson 4 MI/Vocab Add polynomials. Subtract polynomials.

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.

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

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).

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

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

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 ).

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 R = 0.5n n 2 – 3n – 19 T = 0.45n n 2 – 4.4n – 22.6

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 n n Total 0.5n n 2 – 3n–19 – Trad. (–)0.45n n 2 –4.4n–22.6 Video –0.05n n n+ 3.6 Add the opposite. 0.5n n 2 – 3n– 19 (+) –0.45n 3 –1.85n n –0.05n n n+ 3.6

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 If this trend continues, the number of video game sales in 1998 would have been –0.05(2) (2) (2) or 6.2 billion dollars.

1.A 2.B 3.C 4.D Lesson 4 CYP3 A.50x 2 – 50x B.–50x 2 – 50x C.250x x D.50x x 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 x – 300 S = 150x x Find an equation that models the profit.

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?