Standards Lesson Notes

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1 8.2 Add and Subtract Polynomials ink.notebook Page 61 page Add and Subtract Polynomials Lesson Objectives Standards Lesson Objectives Standards Lesson Notes Lesson Notes A.SSE.2 I will rewrite a polynomial into standard form A.APR.1 I will simplify polynomial expressions adding and subtracting like terms 8.2 Adding and Subtracting Polynomials Press the tabs to view details. Press the tabs to view details. 1

2 8.2 Add and Subtract Polynomials ink.notebook Lesson Objectives Standards Lesson Notes A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication add, subtract, and multiply polynomials. Add Polynomials To add polynomials, you can group like terms horizontally or write them in column form, aligning like terms vertically. Like terms are monomial terms that are either identical or differ only in their coefficients, such as 3p and 5p or 2x2y and 8x2y. Press the tabs to view details. Adding Polynomials (Combine like terms) Do NOT change the exponents on the variables *Be careful of negative signs* a) (3x2 + 4x) + (-6x2 + x) b) (5x2-8) + (2x2-3x + 1) 2

3 Subtracting Polynomials Change subtract to add and change the sign on EVERY term in the SECOND polynomial. Then follow the rules of adding c) (3x 2 + 4x) - ( - 6x 2 + x) becomes (3x 2 + 4x) + (6x 2 - x) now combine like terms: d) (5x 2-8) - (2x 2-3x + 1) becomes now combine like terms: 1. (x 2 + y 2 ) + ( x 2 + y 2 ) 4. (2x 2 8) ( 2x 2 6) 2. (2a 8b) ( 3a + 5b) 5. (9xy 2 + 5xy) ( 2xy 8xy 2 ) 3. (2x 2 6) + (5x 2 + 2) + ( x 2 7) 6. (x 2 6x + 2) ( 5x 2 + 7x 4) 3

4 7. (2p 5r) + (3p + 6r) + (p r) 8. (6xy 2 + 4xy) + (2xy 10xy 2 + y 2 ) 9. The measures of two sides of a triangle are given. If P is the perimeter, and P = 10x + 5y, find the measure of the third side. 3x + 4y 5x y 10. The polynomial s 3 70s s 10,800 models the profit a company makes on selling an item at a price s. A second item sold at the same price brings in a profit of s 3 30s s Write a polynomial that expresses the total profit from the sale of both items. 4

5 On Your Whiteboards a) (3a 5) (5a + 1) d) (2x 2 6x 2) + (x 2 + 4x) + (3x 2 + x + 5) b) (9x + 2) ( 3x 2 5) e) (6x 2 5x + 1) ( 7x 2 2x + 4) c) (9xy + y 2x) (6xy 2x) f) (2m 2 + 5m + 1) (4m 2 3m 3) 5

6 On the Worksheet Homework 1. (6x 3 4) + ( 2x 3 + 9) 3. (4 + 2a 2 2a) (3a 2 8a + 7) 4. (8y 4y 2 ) + (3y 9y 2 ) 2. (g 3 2g 2 + 5g) (g 2 + 2g) 6

7 5. ( 4z 3 2z 2 + 8) (4z 3 + 3z 2 5) 7. (2c 2 + 6c + 4) + (5c 2 7) 6. ( 3d d) + (4d 12 + d 2 ) 8. (3n 3 5n + n 2 ) ( 8n 2 + 3n 3 ) 9. (y + 5) + (2y + 4y 2 2) 11. Write the polynomial that represents the perimeter of the figure at the right. 10. (3c 2 c + 11) (c 2 + 2c + 8) 7

8 12. Kim is painting two walls of her bedroom. The area of one wall can be modeled by 3x and the area of the other wall can be modeled by 2x 3. What is the total area? Express the perimeter of each figure as a polynomial in simplest form x-1 5y-3 3x-1 3x-1 4y+2 4y 3x-1 6y-1 Simplify each. 15. t(t 5 )(t 7 ) 16. (5t 5 v 2 )(10t 3 v 4 ) Simplify each

9 19. The total number of students T who traveled for spring break consists of two groups: students who flew to their destinations F and students who drove to their destination D. The number (in thousands) of students who flew and the total number of students who flew or drove can be modeled by the following equations, where n is the number of years since T = 14n + 21 F = 8n + 7 Write an equation that models the number of student who drove to their destination for this time period. 20. From 1997 through 2007, the number of dogs D and the number of cats C (in hundreds) adopted from animal shelters in the United States are modeled by the following equations, where n is the number of years since D = 2n + 3 C = n + 4 Write an equation that models the total number T of dogs and cats adopted in hundreds for this time period. 21. The width of a rectangle is represented by 5x + 2y, and the length is represented by 6y 2x. Write a polynomial that represents the perimeter. 22. The perimeter of the figure at the right is represented by the expression 3x 2 7x + 2. Write a polynomial that represents the measure of the third side 9

10 23. Which ordered pair is in the solution set of the system of inequalities shown in the graph? Answers: a) ( 3, 0) b) (0, 3) c) (5, 0) d) (0, 5) 10