Practice Chapter 7 Test
Name
Date
Tell whether each expression is a monomial.
1. 3a ⫹ 9
3. 11x8
2. 15m5n4
no
yes
4. 9.6z
no
yes
Classify each expression as a monomial, binomial, or trinomial.
Then state its degree.
5. 19a4b3 ⫹ 1
7. 2d9e ⫺ 5d8 ⫹ 13d
6. 2x
binomial; 7th degree
monomial; 1st degree
trinomial; 10th degree
8. 9m4n5 ⫹ 9m12 ⫺ 45
trinomial; 12th degree
Write each polynomial in standard form.
5
9. 5y ⫹ 13 ⫹ 8y3 ⫺ 4y2
9
1
5
10. 16 y ⫺ 4y3 ⫺ 5y5 ⫹ 8
5
15y5 94y3 16
y 58
8y3 4y2 5y 13
11. 8.6n5 ⫺ 1.9n7 ⫺ 14.2n ⫹ 9.8n6
1.9n7 9.8n6 8.6n5 14.2n
Simplify.
12. 19y2 ⫹ 15y ⫺ 24y2 ⫺ 6y
13. 24u ⫹ 19t ⫺ 15u + 7tu ⫹ 8t
4y3 23y2 9y 6
27t 7tu 9u
5y2 9y
16. 8x6y8 ⫺ (5x3y)2(2y6)
15. (5c 8d 9)(⫺2c 6d10)
17. 5x2y7(4x7y2 ⫺ 3x4y3 ⫹ 7xy5)
42x6y8
10c14d19
14. (23y2 ⫺ 12y) ⫺ (4y3 ⫺ 21y ⫹ 6)
20x9y9 15x6y10 35x3y12
Multiply.
19. (x ⫹ 11)(3x ⫺ 4)
Copyright © by William H. Sadlier, Inc. All rights reserved.
18. (7b ⫹ 3)2
(7b 3)(7b 3)
49b2 21b 21b 9
49b2
20. (4x ⫺ 1)(3x ⫺ 2)
3x2 4x 33x 44
42b 9
3x2
12x2 8x 3x 2
29x 44
12x2 11x 2
Find each product.
21. (3b ⫹ 1)(2b2 ⫹ 5b ⫺ 3)
22. (3x2 ⫹ 2x ⫺ 1)(2x2 ⫺ 4x ⫹ 3)
6b3 2b2
15b2 5b
9b 3
6b3 17b2 – 4b 3
6x4 4x3 – 2x2
12x3 8x2 4x
9x2 6x 3
6x4 8x3 x2 10x 3
Divide and check. Check students’ work.
23. 52x3y5 ⫼ 4xy4
24. (16xy4 ⫺ 20x4y3 ⫺ 8x3y2) ⫼ (⫺4x5y2)
13x31y 54
13x2y
4x15y42 5x45y32 2x35y22
4x4y2 5x1y 2x2
5y
4y2
x x22
x4
Lessons 7-1–7-8, pages 176–193.
Chapter 7
191
For More Practice Go To:
Simplify.
11 8
25. u19
y
5 7
( )
26.
( yx )
3
y35
x21
u88
y152
27.
0 2
x21
y35
( 5 3 4)3( 2 5)2
28. c d( e 2 82c4)de
5c d e 3
3g
(18ᐉ
)
5
3(2)g0(2) 36
;
18(2)ᐉ5(2) ᐉ10
c15d9e12(4c4d2e10) 4c13e10
;
125c6d24e12
125d13
36ᐉ10
Divide and check.
30. (a3 ⫹ 4a2 ⫹ 5a ⫹ 2) ⫼ (a ⫹ 2)
a2
4 a2
a 2兲
3
() a 2 a2
2 a2
() 2 a2
a3
z 3
z 4 兲 z2 7 z 2
() z2 4 z
3z 2
() 3 z 12
14
14
z3z4
31. If the perimeter of a square garden is 12a ⫹ 24
units, what is the area of the garden?
Let p 12a 24 and p 4s, where p perimeter,
and s length of a side; Substitute: 12a 24 4s;
Solve for s: s (12a 24) 4 3a 6;
Then find A, such that A s2 (3a 6)2;
(3a 6)2 (3a 6)(3a 6); 9a2 18a 18a 36;
9a2 36a 36; So the area of the garden is
9a2 36a 36 square units.
2a 1
5a 2
5a
4a
a2
() a 2
0
a2 2a 1
32. The diameter of a circular pool is 5x ⫹ 1 units.
What is area of a cover that only fits over the
top of the pool?
5x 1
; A r2; Substitute for r:
2
5x 1 2
25x2 10x 1
A
2
4
1
25 2 5
x x ; The area of the cover is
A
2
4
4
1
25 2 5
x x square units.
2
4
4
r
(
(
)
(
)
)
Explain how you solve the problem. Show all your work. Answers may vary. Check students’ work.
33. What is area of the shaded region?
Find the area of each square.
Area of large square: (5x 2)(5x 2) 25x2 20x 4;
area of small squares: (x 3)(x 3) x2 6x 9 and
(x 1)(x 1) x2 2x 1;
Add the area of the two small squares:
(x2 6x 9) (x2 2x 1) 2x2 8x 10;
Subtract the total area of the smaller squares from the area of the large
square: (25x2 20x 4) (2x2 8x 10) 23x2 12x 6.
192
Chapter 7
5x ⫹ 2
x⫹3
5x ⫹ 2
x⫹3
x⫹1
x⫹1
Copyright © by William H. Sadlier, Inc. All rights reserved.
29. (z2 ⫹ 7z ⫺ 2) ⫼ (z ⫹ 4)