Download Name Date Class Understanding Polynomial Expressions Review

Name _______________________________________ Date __________________ Class __________________
LESSON
17-1
Understanding Polynomial Expressions
Review
Identify each expression as a monomial, a binomial, a trinomial, or
none of the above. Write the degree of each expression.
1. 6b2 7
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3. 35r3s
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5. 4ab5  2ab  3a4b3
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2. x2y  9x4y2  3xy
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4. 3p 
2p
 5q
q
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6. st  t 0.5
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Simplify each expression.
7. 6n3  n2  3n4  5n2
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9. 11b2 3b  1  2b2  2b  8
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11. 9xy  5x2  15x  10xy
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8. c3  c2  2c  3c3  c2  4c
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10. a4b3  9a3b4  3a4b3  4a3b4
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12. 3p2q  8p3  2p2q  2p  5p3
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Determine the polynomial that has the greater value for the given
value of x.
13. 4x2  5x  2 or 5x2  2x  4 for x  6
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14. 6x3  4x2  7 or 7x3  6x2  4 for x  3
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Name _______________________________________ Date __________________ Class __________________
Solve.
15. A rocket is launched from the top of an 80-foot cliff with an initial
velocity of 88 feet per second. The height of the rocket t seconds
after launch is given by the equation h  16t2  88t  80. How high
will the rocket be after 2 seconds?
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16. Antoine is making a banner in the shape of a triangle. He wants to
line the banner with a decorative border. How long will the border be?
LESSON
17-2
Adding Polynomial Expressions
Review
Add the polynomial expressions using the vertical format.
1.
(10g 2  3g  10)
 (2g 2  g  9)
2.
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3.
(11b2  3b  1)
 (2b2  2b  8)
5.
 (3ab 2  a  7b )
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 (3 x 3  x 2  4 x )
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4.
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(ab 2  13b  4a )
(4 x 3  x 2  2 x )
( c 3  2c 2  2c )
 ( 3c 3  c 2  4c )
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6.
( r 2  8 pr  p )
 ( 12r 2  2 pr  8 p )
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Name _______________________________________ Date __________________ Class __________________
Add the polynomial expressions using the horizontal format.
7. (3y2 y  3)  (2y2  2y  9)
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9. (6s3  9s  10)  (3s3  4s  10)
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11. (7a2b3  3a3b  9ab)  (4a2b3  5a3b  ab)
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8. (4z3  3z2  8)  (2z3  z2  3)
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10. (15a4  6a2  a)  (6a4  2a2  a)
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12. (2p4q2  5p3q  2pq)  (8p4q2  3p3q  pq)
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Solve.
13. A rectangular picture frame has the dimensions shown in
the figure. Write a polynomial that represents the perimeter
of the frame.
Name _______________________________________ Date __________________ Class __________________
LESSON
17-3
Subtracting Polynomial Expressions
Review
Subtract using the vertical form.
1.
(5g 2  6g  10)
 (2g 2  2g  9)
2.
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3.
(10b 2  5b  2)
 ( 2b 2  b  1)
(14ab 2  9b  2a )
 ( 4ab 2  2a  5b )
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 (2 x 3  x 2  x )
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4.
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5.
(8 x 3  4 x 2  x )
( 7c 3  5c 2  2c )
 ( 3c 3  2c 2  2c )
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6.
(6 x 3  2 x 2  3 x )
 (3 x 3  2 x 2  3 x )
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Subtract using the horizontal form.
7. (7y2  7y  7)  (4y2  2y  3)
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9. (9s3  10s  8)  (2s3  9s  11)
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11. (a2b3  a3b  ab)  (a2b3  a3b  ab)
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8. (11z3  6z2  3)  (9z3  2z2  8)
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10. (25a4  9a2  3a)  (24a4  5a2  3a)
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12. (3p4q2  8p3q  2)  (5p4q2  2p3q  8)
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Name _______________________________________ Date __________________ Class __________________
Solve.
13. Darnell and Stephanie have competing refreshment stand businesses.
Darnell’s profit can be modeled with the polynomial c2  8c  100,
where c is the number of items sold. Stephanie’s profit can be modeled
with the polynomial 2c2  7c  200. Write a polynomial that represents
the difference between Stephanie’s profit and Darnell’s profit.
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14. There are two boxes in a storage unit. The volume of the first box is
4x3  4x 2 cubic units. The volume of the second box is 6 x 3  18 x 2
cubic units. Write a polynomial to show the difference between the two
volumes.
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Name _______________________________________ Date __________________ Class __________________
LESSON 17-1
1.binomial; degree 2
2. trinomial; degree 6
3. monomial; degree 4
4. none of the above
5. trinomial; degree 7
7. 3y2  9y  4
8. 2z3  4z2  11
9. 7s3  s  19
10. a4  14a2
11. 2(a2)(b3)  2(a3)b  2ab
12. 2p4q2  10p3q  6
6. none of the above
13. c2  15c  100
7. 3n4  6n3  4n2
14. 2x3  22x2
8. 2c3  2c
9. 9b2  b  9
10. 2a4b3  5a3b4
11. 5x2  15x  xy
12. p2q  13p3  2p
13. 5x2 2x  4
14. 7x3 6x2  4
15. 192 ft
16. 33b  8
LESSON 17-2
1. 12g2  4g  1
2. 7x3  2x2  6x
3. 13b2  5b  7
4. 2c3  3c2  2c
5. 4ab2  20b  3a
6. 13r2  6pr  7p
7. 5y2  y  12
8. 6z3  4z2  5
9. 9s3  13s
10. 21a4  4a2  2a
11. 3a2b3  2a3b  8ab
12. 10p4q2  2p3q  3pq
13. 16x  2
LESSON 17-3
1. 3g2  4g  19
2. 6x3  3x2
3. 8b2  4b  3
4. 10c3  7c2  4c
5. 10ab2  4b  4a
6. 3x3  4x2 6x