8.2 Adding and Subtracting Polynomials
Learning Objective: A.SSE.2
A.APR.1
NAME _______________________________
I will rewrite a polynomial into standard form
I will simplify polynomial expressions adding and subtracting like terms
Find each sum or difference.
1. (6x3 – 4) + (–2x3 + 9)
2. (g3 – 2g2 + 5g) – (g2 + 2g)
3. (4 + 2a2 – 2a) – (3a2 – 8a + 7)
4. (8y – 4y2) + (3y – 9y2)
5. (–4z3 – 2z2 + 8) – (4z3 + 3z2 – 5)
6. (–3d2 – 8 + 2d) + (4d – 12 + d2)
7. (2c2 + 6c + 4) + (5c2 – 7)
8. (3n3 – 5n + n2) – (–8n2 + 3n3)
9. (y + 5) + (2y + 4y2 – 2)
10. (3c2 – c + 11) – (c2 + 2c + 8)
11. Write the polynomial that represents the
perimeter of the figure at the right.
12. Kim is painting two walls of her bedroom. The area of one wall can be modeled by 3x2 + 14
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.
13.
14.
Put into slope-intercept form. (Solve each equation for y.)
15. y – 3x = 6
16. 6y = 12x + 24
18. y – 7 = 5x
17. 3y + 12 = 9x
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 1995.
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 1997.
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
3x2 – 7x + 2. Write a polynomial that represents the measure of the
third side.
23. Which ordered pair is in the solution set of the system
of inequalities shown in the graph?
a) (–3, 0)
b) (0, –3)
c) (5, 0)
d) (0, 5)
Answers: 1) 4x3 + 5
11) 12x + 1
1
4
3) –a2 + 6a – 3
13) 12x – 4
5) –8z3 – 5z2 + 13
15) y = 3x + 6
7) 7c2 + 6c – 3
17) y = 3x – 4
9) 4y2 + 3y + 3
19) D = 6n + 14
21) 6x + 16y
23) C