Name
8-1
Class
Date
Practice
Form G
Adding and Subtracting Polynomials
Find the degree of each monomial.
1. 2b2c2 4
2. 5x 1
3. 7y5 5
4. 19ab 2
5. 12 0
1
6. 2 z2 2
7. t 1
8. 4d4e 5
Simplify.
9. 2a3b 1 4a3b 6a3b
12. 26ab 1 3ab 23ab
10. 5x3 2 4x3 x3
11. 3m6n3 2 5m6n3 22m6n3
13. 4c2d6 2 7c2d6 23c2d6
14. 315x2 2 30x2 285x2
Write each polynomial in standard form. Then name each polynomial based on
its degree and number of terms.
15. 15x 2 x3 1 3
2x3 1 15x 1 3; cubic
trinomial
18. 7b2 1 4b
7b2 1 4b; quadratic
binomial
16. 5x 1 2x2 2 x 1 3x4
3x4 1 2x2 1 4x; fourth
degree trinomial
19. 23x2 1 11 1 10x
23x2 1 10x 1 11;
quadratic trinomial
17. 9x3
9x3 ; cubic monomial
20. 12t2 1 1 2 3x 1 8 2 2x
12t2 2 5x 1 9;
quadratic trinomial
Simplify.
21.
8z 2 12
1 6z 1 90
22.
14z 2 3
24. (3k2 1 5) 1 (16x2 1 7)
9x3 1 3
1 4x3 1 7
13x3 1 10
3k2 1 16x2 1 12
23.
6j2 2 2j 1 5
1 3j 2 1 4j 2 6
9j2 1 2j 2 1
25. (g4 2 4g2 1 11) 1 (2g3 1 8g)
g4 2 g3 2 4g2 1 8g 1 11
26. A local deli kept track of the sandwiches it sold for three months. The
polynomials below model the number of sandwiches sold, where s
represents days.
Ham and Cheese:
Pastrami:
4s3 2 28s2 1 33s 1 250
27.4s2 1 32s 1 180
Write a polynomial that models the total number of these sandwiches that
were sold. 4s3 2 35.4s2 1 65s 1 430
Prentice Hall Gold Algebra 1 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
3
Name
Class
8-1
Date
Practice (continued)
Form G
Adding and Subtracting Polynomials
Simplify.
7x4 1 9
28.
2 (8x4 1 2)
11n 2 4
27.
2 (5n 1 2)
6n 2 6
29.
3d2 1 8d 2 2
2 (2d2 2 7d 1 6)
2x4 1 7
30. (28e3 1 3e2) 1 (19e3 1 e2)
d2 1 15d 2 8
31. (212h4 1 h) 2 (26h4 1 3h2 2 4h)
47e3 1 4e2
26h4 2 3h2 1 5h
32. A small town wants to compare the number of students enrolled in public and
private schools. The polynomials below show the enrollment for each:
Public School:
Private School:
219c2 1 980c 1 48,989
40c 1 4046
Write a polynomial for how many more students are enrolled in public school
than private school. 219c2 1 940c 1 44,943
Simplify. Write each answer in standard form.
33. (3a2 1 a 1 5) 2 (2a 2 5)
34. (6d 2 10d3 1 3d2) 2 (5d3 1 3d 2 4)
3a2 2 a 1 10
215d3 1 3d2 1 3d 1 4
35. (24s3 1 2s 2 3) 1 (22s2 1 s 1 7)
36. (8p3 2 6p 1 2p2) 1 (9p2 2 5p 2 11)
24s3 2 2s2 1 3s 1 4
8p3 1 11p2 2 11p 2 11
37. The fence around a quadrilateral-shaped pasture is
3a2 1 15a 1 9 long. Three sides of the fence have the
following lengths: 5a, 10a 2 2, a2 2 7. What is the length
of the fourth side of the fence?
5a
2a2 1 18
?
a2 ź7
10a ź2
38. Error Analysis Describe and correct the error in
simplifying the sum shown at the right.
6x3
two unlike terms,
6x3 2 3x2 1 6x 2 2
and
23x2 ,
were added;
6x3 + 4x – 10
+ (–3x2 + 2x + 8)
3x3 + 6x – 2
39. Open-Ended Write three different examples of the sum of a
quadratic trinomial and a cubic monomial.
Answers may vary. Sample: (x2 1 2x 1 1) 1 x3 ;
(2x2 1 5x 1 6) 1 3x3 ; (r2 1 r 1 1) 1 8r3
Prentice Hall Gold Algebra 1 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
4