Lesson 4 Menu : Lesson 4 Menu Five-Minute Check (over Lesson 7-3)
Main Ideas
California Standards
Example 1: Add Polynomials
Example 2: Subtract Polynomials
Example 3: Real-World Example
Lesson 4 MI/Vocab : Lesson 4 MI/Vocab Add polynomials. Subtract polynomials.
Lesson 4 CA : Lesson 4 CA Standard 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques. (Key, CAHSEE)
Lesson 4 Ex1 : Lesson 4 Ex1 Add Polynomials Find (7y2 + 2y – 3) + (2 – 4y + 5y2). Method 1 Horizontal (7y2 + 2y – 3) + (2 – 4y + 5y2)
= (7y2 + 5y2) + [2y + (–4y) + [(– 3) + 2] Group like terms.
= 12y2 – 2y – 1 Add like terms.
Lesson 4 Ex1 : Lesson 4 Ex1 Add Polynomials Method 2 Vertical Answer: 12y2 – 2y – 1 Notice that terms are in descending order with like terms aligned. 12y2 – 2y – 1
Slide 6 : A
B
C
D A. –2x2 + 5x + 3
B. 8x2 + 6x – 4
C. 2x2 + 5x + 4
D. –15x2 + 6x – 4 Find (3x2 + 2x – 1) + (–5x2 + 3x + 4).
Lesson 4 Ex2 : Lesson 4 Ex2 Subtract Polynomials Find (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2). Method 1 Horizontal Subtract 9y4 – 7y +2y2 by adding its additive inverse.
(6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2)
= (6y2 + 8y4 – 5y) + (–9y4 + 7y – 2y2)
= [8y4 + (–9y4)] + [6y2 + (–2y2)] + (–5y + 7y)
= –y4 + 4y2 + 2y
Lesson 4 Ex2 : Lesson 4 Ex2 Subtract Polynomials Method 2 Vertical Align like terms in columns and subtract by adding the additive inverse. Answer: 4y2 – y4 + 2y or –y4 + 4y2 + 2y
Slide 9 : A
B
C
D A. 2x2 + 7x3 – 3x4
B. x4 – 2x3 + x2
C. x2 + 8x3 – 3x4
D. 3x4 + 2x3 + x2 Find (3x3 + 2x2 – x4) – (x2 + 5x3– 2x4).
Lesson 4 Ex3 : Lesson 4 Ex3 A. VIDEO GAMES The total amount of toy sales T (in billions of dollars) consists of two groups: sales of video games V and sales of 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 = 0.5n3 + 1.9n2 + 3n + 19
T = 0.45n3 + 1.85n2 + 4.4n + 22.6
Lesson 4 Ex3 : Lesson 4 Ex3 Find an equation that models the sales of video games V. Subtract the polynomial for R from the polynomial for T. Answer: V = –0.05n3 + 0.05n2 + 1.4n + 3.6
Lesson 4 Ex3 : 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.
Slide 13 : A
B
C
D A. 50x2 – 50x + 500
B. –50x2 – 50x + 500
C. 250x2 + 950x + 500
D. 50x2 + 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 = 100x2 + 500x – 300S = 150x2 + 450x + 200Find an equation that models the profit.
Slide 14 : A
B
C
D 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?
End of Lesson 4 : End of Lesson 4