Name Class Date Practice
Form G
Adding and Subtracting Polynomials
Find the degree of each monomial.
1. 2b2c2 4
2. 5x 1
3. 7y 5 5
4. 19ab 2
5. 12 0
2
6. 1
2z 2
7. t 1
8. 4d 4e 5
Simplify.
9. 2a3b + 4a3b
12. -6ab + 3ab
6a3b
3
10. 5x 3 - 4x3 x
11. 3m6n3 - 5m6n3
−2m6n3
−3ab
13. 4c2d 6 - 7c2d 6 −3c 2d 6
14. 315x 2 - 30x 2 285x 2
Write each polynomial in standard form. Then name each polynomial based on
its degree and number of terms.
15. 15x - x3 + 3
−x 3 + 15x + 3; cubic
trinomial
18. 7b2 + 4b
7b2 + 4b; quadratic
binomial
16. 5x + 2x 2 - x + 3x4
3x 4 + 2x 2 + 4x; fourth
degree trinomial
19. -3x2 + 11 + 10x
−3x 2 + 10x + 11;
quadratic trinomial
17. 9x 3
9x 3 ; cubic monomial
20. 12t 2 + 1 - 3x + 8 - 2x
12t 2 − 5x + 9;
quadratic trinomial
Simplify.
21.
8z - 12
+ 6z + 90
14z − 3
22.
9x3 + 3
+ 4x3 + 7
23.
13x 3 + 10
6j 2 - 2j + 5
+ 3j 2 + 4j - 6
9j 2 + 2j − 1
24. (3k 2 + 5) + (16x 2 + 7)
25. (g 4 - 4g 2 + 11) + (-g 3 + 8g)
3k 2 + 16x 2 + 12
g4 − g3 − 4g2 + 8g + 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 - 28s2 + 33s + 250
-7.4s2 + 32s + 180
Write a polynomial that models the total number of these sandwiches that
were sold. 4s3 - 35.4s2 + 65s + 430
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Name Class Date Practice (continued)
Form G
Adding and Subtracting Polynomials
Simplify.
27.
11n - 4
28.
- (5n + 2)
7x4 + 9
29.
- (8x4 + 2)
6n − 6
3d 2 + 8d - 2
- (2d 2 - 7d + 6)
−x 4 + 7
30. (28e3 + 3e2) + (19e3 + e2)
47e3 + 4e2
d 2 + 15d − 8
31. (-12h4 + h) - (-6h4 + 3h2 - 4h)
−6h4 − 3h2 + 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:
-19c2 + 980c + 48,989
40c + 4046
Write a polynomial for how many more students are enrolled in public school
than private school. −19c 2 + 940c + 44,943
Simplify. Write each answer in standard form.
33. (3a2 + a + 5) - (2a - 5)
3a2 − a + 10
34. (6d - 10d 3 + 3d 2) - (5d 3 + 3d - 4)
−15d 3 + 3d 2 + 3d + 4
35. (-4s3 + 2s - 3) + (-2s2 + s + 7)
36. (8p3 - 6p + 2p2) + (9p2 - 5p - 11)
−4s3 − 2s2 + 3s + 4
8p3 + 11p2 − 11p − 11
37. The fence around a quadrilateral-shaped pasture is
3a2 + 15a + 9 long. Three sides of the fence have the
following lengths: 5a, 10a - 2, a2 - 7. What is the length of
the fourth side of the fence?
5a
2a2 + 18
?
a2 − 7
10a − 2
38. Error Analysis Describe and correct the error in
simplifying the sum shown at the right.
6x 3
two unlike terms,
6x 3 − 3x 2 + 6x − 2
and
−3x 2 ,
were added;
6x3 + 4x – 10
+ (–3x2 + 2x + 8)
39. Open-Ended Write three different examples of the sum of a
quadratic trinomial and a cubic monomial.
Answers may vary. Sample: (x 2 + 2x + 1) + x 3 ;
(2x 2 + 5x + 6) + 3x 3 ; (r 2 + r + 1) + 8r 3
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3x3 + 6x – 2
Name Class Date Practice
Form K
Adding and Subtracting Polynomials
Find the degree of each monomial.
1. 3s3t 3 6
2. 3n 1
3. 5xy 2
4. 7 0
5
5. 1
4k 5
6. d 1
Simplify.
7. 3mn4 + 6mn4
9mn4
9. -11c4d + 12c4d
c 4d
8. 12g 2 - 7g 2 5g2
10. 42z 3 - 15z 3 27z 3
Write each polynomial in standard form. Then name each polynomial based on
its degree and number of terms.
11. 7a + 4 - a2
12. 5b2 + 2n
−a2 + 7a + 4; quadratic trinomial
13. -11d 4
5b2 + 2n; quadratic binomial
14. 2x 3 - 9 + 2x + 8 - 4x
−11d 4 ; 4th degree monomial
2x 3 − 2x − 1; cubic trinomial
15. A pizza shop owner is monitoring the amount of cheese he uses each week.
The polynomials below model the pounds of cheese ordered in the past,
where p represents pounds.
Mozzarella: 3p3 - 6p2 + 14p + 125
Cheddar: 12.5p2 + 18p + 75
Write a polynomial that models the total number of pounds of cheese that
were ordered.
3p3 + 6.5p2 + 32p + 200
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Name Class Date Practice (continued)
Form K
Adding and Subtracting Polynomials
Simplify.
16.
3r + 5
+ 7r + 3
17. (t 4 - 4t 2 + 9) + (-t 3 + 3t)
7b2 + 6
+ 4b2 + 5
19.
10r + 8
18.
t 4 − t 3 − 4t 2 + 3t + 9
4z + 7
- (6z + 1)
−2z + 6
11b2 + 11
20. (-6k 3
+ 3k) -
(-5k 3
+
3k 2
- 8k)
3p4 + 1
21.
- (9p4 + 5)
−6p4 − 4
−k 3 − 3k 2 + 11k
22. A city wants to compare the number of people who own their own home and
who rent their home. The polynomials below show expressions for each. In
each polynomial, p = 0 corresponds to the first year.
Own: 4p2 + 360p + 22,178
Rent: 6p2 + 125p + 5286
Write a polynomial for how many more own their home than rent their home.
−2p2 + 235p + 16,892
23. The wallpaper border that runs all the way around a room is 5f 2 + 19f + 11
long. Three sides of the room have the following lengths of border: 6f, 5f - 7,
2f 2 + 2. What is the length of the fourth side of the room?
3f 2 + 8f + 16
24. Open-Ended Write two different polynomials with a difference of
-3x2 + 5x - 7.
Answers may vary. Sample: ( −1x 2 + 6x − 4) − (2x 2 + x + 3) and
(−4x 2 + 7x − 5) − ( −x 2 + 2x + 2)
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