7-7 Divide a Polynomial by a Monomial
Name
Date
Divide: (15y3 ⫹ 20y2 ⫺ 30y) ⫼ 5y
15y3
20y2
15y3 ⫹ 20y2 ⫺ 30y
⫺30y
⫽
⫹
⫹
5y
5y
5y
5y
( ) ( ) (
)
Divide each term of the polynomial by the monomial divisor.
⫽ (3y31) ⫹ (4y21) ⫹ (⫺6y11)
⫽ 3y2 ⫹ 4y ⫺ 6
Divide the coefficients; apply the Law of Exponents for
Division to divide the variables.
Simplify.
So (15y3 ⫹ 20y2 ⫺ 30y) ⫼ 5y ⫽ 3y2 ⫹ 4y ⫺ 6.
y⫺2
Simplify: ⫺3
z
2
( )
y⫺2
z⫺3
( )
2
⫽
y⫺2(2)
z⫺3(2)
Use the Law of Exponents for a Power of a Quotient.
3(2)
⫽ z2(2)
y
Use the Law of Exponents for a Negative Power.
6
⫽ z4
y
Simplify by raising a power to a power.
Divide and check. Check students’ work.
1. 12v7 ⫼ (⫺6v5) 12 v7
(6)(v )
5
2. 40b9 ⫼ (⫺5b3)
9
2v7 5
?
40 b
(5
)( b )
2v2
Copyright © by William H. Sadlier, Inc. All rights reserved.
3 6
60 g h
4 gh4
( )(
2 4
(63)( xxyy )
3
8b9 3
12v7 (6v5)(2v2)
12v7 12v7 True
4. 60g3h6 ⫼ 4gh4
3. 6x2y4 ⫼ 3xy2
2
8b6
2xy2
5. ⫺126a11bc2 ⫼ 14ab4c6
a bc
(126
14 )( ab c )
11
)
4 6
9a10
15g2h2
7. (15x3 ⫹ 25x2 ⫺ 2x) ⫼ (⫺5x)
3x2 5x 2
5
2
b3c4
8. (28y3 ⫹ 12y2 ⫺ 5y) ⫼ (⫺4y)
7y2 3y 5
4
10. (12m6n4 ⫺ 30m5n7 ⫺ 42m4n6) ⫼ (⫺6m4n6)
6. –236pq4r11 ⫼ 59p3q7r9
4 11
pq r
(236
59 )( p q r )
3 7 9
4r2
p2q3
9. (4x4 ⫺ 12x3y2 ⫺ 10x2y) ⫼ (⫺2x2y)
2x2 6xy 5
y
11. (52r7s5t4 ⫺ 91r9s7t2 ⫹ 78r8s7t3) ⫼ (⫺13r8s6t3)
4t 7rs 6s
t
rs
2m2 5mn 7
n2
Lesson 7-7, pages 190–191.
Chapter 7
181
For More Practice Go To:
Simplify.
5
13. v11
w
x3 4
x 3(4)
2(4)
y
0
16. 4w
6
v
x12
y8
0
17. ⫺2a
b3
(
4313
v18
64v18
(⫺4m4n2)2(2mn)3
⫺20m5n10
21.
(16m8n4)(8m3n3)
20m5n10
20m5n10
24.
;
32m6
5n3
(3x2y2)2(⫺xy3)4
(7x3y2)3 (x3y2)3
(32x4y4)(x4y12)
(73x9y 6)(x9y6)
73y 8 343y8
;
32
9
b12
15x12y4
144x10y18 48y14
;
15x12y4 5x2
22.
5
19. ⫺36v8
⫺6t
3
(
(2b
)
a
3 3
2
9
23.
0.16c6d24
(2r2s2)3(⫺rs7)2
⫺(9r2s3)2(r4s)2
(23r6s6)(r2s14)
(92r4s6)(r8s2)
(23r4s8)
81s4
;
2
4
4
(9 r s )
8
;
5
(⫺3.2x8y6)2(x3y4)3
(1.6x14y10)2
2.56x28y20
10.24x25y24 4y4
;
2.56x28y20
x3
144c26
d2
26.
8 4
(6tv )
(10.24x16y12)(x9y12)
(16c24d20)(1.44c8d2)
0.16c6d24
4
)
32
1296t
20
v
(2c6d5)4(1.2c4d)2
(⫺0.4c3d12)2
23.04c32d22
d5(13)
e8(13)
65
d104
e
8b
a6
16b12
(16x8y16)(9x2y2)
)
(2)414
(2x2y4)4(⫺3xy)2
⫺15x12y4
25.
b3(2)
c5(2)
6
b10
c
(
13
( )
2
18. ⫺14a
7b3
4
)
128m11n7
v5(12)
w11(12)
60
v132
w
3
5
15. d8
e
2
( )
( )
20.
3
14. b5
c
12
( )
12. (y2)
(⫺3p4q2)2(p2q)3
(4p8q3)2(⫺p4q5)3
(32)p8q4p6q3
(4)2p16q6(p12q15)
16p2q1 16p2q8
;
9p4q9
9
27. The area of a rectangle with width 3x is given by
the expression 12x2 ⫺ 15x. Write a polynomial
expression for the length of the rectangle.
Divide: (12x2 15x) 3x;
12x2 3x 15x 3x; 4x 5;
The length of the rectangle can be represented
by the binomial 4x 5.
28. The area of a triangle with height 4x is given by
the expression 16x2 ⫺ 4x. Write a polynomial
expression for the base of the triangle.
1
A bh, and h 4x and A 16x2 4x;
2
1
Substitute: 16x2 4x b(4x); Solve for b:
2
16x2 4x 2x(b); b (16x2 4x) 2x; b 8x 2;
The base of the triangle can be represented
by the binomial 8x 2.
Compute mentally.
29. (24)(30)
(20 4)30 20 • 30 4 • 30 600 120 720
182
Chapter 7
30. (15)(9)(2)
(15)(2)(9) (30)(9) 270
2
1
1
1
31. 5 3 ⫹ 7 8 ⫹ 11 3 ⫺ 4 8
1
1
1
2
5 11 7 4 3
8
8
3
17 3 20
Copyright © by William H. Sadlier, Inc. All rights reserved.
Solve.