Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Division of Algebraic Expressions - Exercise 8.4
Division of Algebraic Expressions - Exercise 8.4 | Mathematics (Maths) Class 8 PDF Download
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Page 1
Question:18
Divide 5x
3
- 15x
2
+ 25x by 5x.
Solution:
Question:19
Divide 4z
3
+ 6z
2
- z by -
1
2
z.
Solution:
Question:20
Divide 9x
2
y - 6xy + 12xy
2
by -
3
2
xy.
Solution:
Question:21
Divide 3x
3
y
2
+ 2x
2
y + 15xy by 3xy.
Solution:
Question:22
Divide x
2
+ 7x + 12 by x + 4.
Solution:
Question:23
Divide 4y
2
+ 3y +
1
2
by 2y + 1.
Solution:
Page 2
Question:18
Divide 5x
3
- 15x
2
+ 25x by 5x.
Solution:
Question:19
Divide 4z
3
+ 6z
2
- z by -
1
2
z.
Solution:
Question:20
Divide 9x
2
y - 6xy + 12xy
2
by -
3
2
xy.
Solution:
Question:21
Divide 3x
3
y
2
+ 2x
2
y + 15xy by 3xy.
Solution:
Question:22
Divide x
2
+ 7x + 12 by x + 4.
Solution:
Question:23
Divide 4y
2
+ 3y +
1
2
by 2y + 1.
Solution:
Question:24
Divide 3x
3
+ 4x
2
+ 5x + 18 by x + 2.
Solution:
Question:25
Divide 14x
2
- 53x + 45 by 7x - 9.
Solution:
Question:26
Divide -21 + 71x - 31x
2
- 24x
3
by 3 - 8x.
Solution:
Question:27
Divide 3y
4
- 3y
3
- 4y
2
- 4y by y
2
- 2y.
Solution:
Question:28
Divide 2y
5
+ 10y
4
+ 6y
3
+ y
2
+ 5y + 3 by 2y
3
+ 1.
Solution:
Question:29
Divide x
4
- 2x
3
+ 2x
2
+ x + 4 by x
2
+ x + 1.
Solution:
Question:30
Divide m
3
- 14m
2
+ 37m - 26 by m
2
- 12m +13.
Solution:
Page 3
Question:18
Divide 5x
3
- 15x
2
+ 25x by 5x.
Solution:
Question:19
Divide 4z
3
+ 6z
2
- z by -
1
2
z.
Solution:
Question:20
Divide 9x
2
y - 6xy + 12xy
2
by -
3
2
xy.
Solution:
Question:21
Divide 3x
3
y
2
+ 2x
2
y + 15xy by 3xy.
Solution:
Question:22
Divide x
2
+ 7x + 12 by x + 4.
Solution:
Question:23
Divide 4y
2
+ 3y +
1
2
by 2y + 1.
Solution:
Question:24
Divide 3x
3
+ 4x
2
+ 5x + 18 by x + 2.
Solution:
Question:25
Divide 14x
2
- 53x + 45 by 7x - 9.
Solution:
Question:26
Divide -21 + 71x - 31x
2
- 24x
3
by 3 - 8x.
Solution:
Question:27
Divide 3y
4
- 3y
3
- 4y
2
- 4y by y
2
- 2y.
Solution:
Question:28
Divide 2y
5
+ 10y
4
+ 6y
3
+ y
2
+ 5y + 3 by 2y
3
+ 1.
Solution:
Question:29
Divide x
4
- 2x
3
+ 2x
2
+ x + 4 by x
2
+ x + 1.
Solution:
Question:30
Divide m
3
- 14m
2
+ 37m - 26 by m
2
- 12m +13.
Solution:
Question:31
Divide x
4
+ x
2
+ 1 by x
2
+ x + 1.
Solution:
Question:32
Divide x
5
+ x
4
+ x
3
+ x
2
+ x + 1 by x
3
+ 1.
Solution:
Question:33
Divide 14x
3
- 5x
2
+ 9x - 1 by 2x - 1 and find the quotient and remainder
Solution:
Quotient = 7x
2
+ x + 5Remainder = 4
Question:34
Divide 6x
3
- x
2
- 10x - 3 by 2x - 3 and find the quotient and remainder.
Solution:
Quotient = 3x
2
+ 4x + 1 Remainder = 0
Question:35
Divide 6x
3
+ 11x
2
- 39x - 65 by 3x
2
+ 13x + 13 and find the quotient and remainder.
Solution:
Quotient = 2x -5Remainder = 0
Question:36
Divide 30x
4
+ 11x
3
- 82x
2
- 12x + 48 by 3x
2
+ 2x - 4 and find the quotient and remainder.
Solution:
Quotient = 10x
2
-3x -12Remainder = 0
Page 4
Question:18
Divide 5x
3
- 15x
2
+ 25x by 5x.
Solution:
Question:19
Divide 4z
3
+ 6z
2
- z by -
1
2
z.
Solution:
Question:20
Divide 9x
2
y - 6xy + 12xy
2
by -
3
2
xy.
Solution:
Question:21
Divide 3x
3
y
2
+ 2x
2
y + 15xy by 3xy.
Solution:
Question:22
Divide x
2
+ 7x + 12 by x + 4.
Solution:
Question:23
Divide 4y
2
+ 3y +
1
2
by 2y + 1.
Solution:
Question:24
Divide 3x
3
+ 4x
2
+ 5x + 18 by x + 2.
Solution:
Question:25
Divide 14x
2
- 53x + 45 by 7x - 9.
Solution:
Question:26
Divide -21 + 71x - 31x
2
- 24x
3
by 3 - 8x.
Solution:
Question:27
Divide 3y
4
- 3y
3
- 4y
2
- 4y by y
2
- 2y.
Solution:
Question:28
Divide 2y
5
+ 10y
4
+ 6y
3
+ y
2
+ 5y + 3 by 2y
3
+ 1.
Solution:
Question:29
Divide x
4
- 2x
3
+ 2x
2
+ x + 4 by x
2
+ x + 1.
Solution:
Question:30
Divide m
3
- 14m
2
+ 37m - 26 by m
2
- 12m +13.
Solution:
Question:31
Divide x
4
+ x
2
+ 1 by x
2
+ x + 1.
Solution:
Question:32
Divide x
5
+ x
4
+ x
3
+ x
2
+ x + 1 by x
3
+ 1.
Solution:
Question:33
Divide 14x
3
- 5x
2
+ 9x - 1 by 2x - 1 and find the quotient and remainder
Solution:
Quotient = 7x
2
+ x + 5Remainder = 4
Question:34
Divide 6x
3
- x
2
- 10x - 3 by 2x - 3 and find the quotient and remainder.
Solution:
Quotient = 3x
2
+ 4x + 1 Remainder = 0
Question:35
Divide 6x
3
+ 11x
2
- 39x - 65 by 3x
2
+ 13x + 13 and find the quotient and remainder.
Solution:
Quotient = 2x -5Remainder = 0
Question:36
Divide 30x
4
+ 11x
3
- 82x
2
- 12x + 48 by 3x
2
+ 2x - 4 and find the quotient and remainder.
Solution:
Quotient = 10x
2
-3x -12Remainder = 0
Question:37
Divide 9x
4
- 4x
2
+ 4 by 3x
2
- 4x + 2 and find the quotient and remainder.
Solution:
?
Quotient = 3x
2
+ 4x + 2 and remainder = 0.
Question:38
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
Dividend Divisor
i 14x
2
+ 13x - 15 7x - 4
ii 15z
3
- 20z
2
+ 13z - 12 3z - 6
iii 6y
5
- 28y
3
+ 3y
2
+ 30y - 9 2y
2
- 6
iv 34x - 22x
3
- 12x
4
- 10x
2
- 75 3x + 7
v 15y
4
- 16y
3
+ 9y2 -
10
3
y + 6
3y - 2
vi 4y
3
+ 8y + 8y
2
+ 7 2y
2
- y + 1
vii 6y
5
+ 4y
4
+ 4y
3
+ 7y
2
+ 27y + 6 2y
3
+ 1
Solution:
i
Quotient = 2x + 3
Remainder = -
3
Divisor = 7x -
4
Divisor ×
Quotient + Remainder = (7x -
4) (2x + 3) -
?3
= 14x
2
+ 21x -
8x -
12 -
?3
= 14x
2
+ 13x -
15
= Dividend
Thus,
Divisor ×
Quotient + Remainder = Dividend
Hence verified.
ii
Quotient = 5z
2
+
10
3
z +11Remainder = 54Divisor = 3z -6Divisor × Quotient +Remainder = 3z -6 5z
2
+
10
3
z +11 +54 = 15z
3
+10z
2
+33z -30z
2
-
Hence verified.
( ) ( )
Page 5
Question:18
Divide 5x
3
- 15x
2
+ 25x by 5x.
Solution:
Question:19
Divide 4z
3
+ 6z
2
- z by -
1
2
z.
Solution:
Question:20
Divide 9x
2
y - 6xy + 12xy
2
by -
3
2
xy.
Solution:
Question:21
Divide 3x
3
y
2
+ 2x
2
y + 15xy by 3xy.
Solution:
Question:22
Divide x
2
+ 7x + 12 by x + 4.
Solution:
Question:23
Divide 4y
2
+ 3y +
1
2
by 2y + 1.
Solution:
Question:24
Divide 3x
3
+ 4x
2
+ 5x + 18 by x + 2.
Solution:
Question:25
Divide 14x
2
- 53x + 45 by 7x - 9.
Solution:
Question:26
Divide -21 + 71x - 31x
2
- 24x
3
by 3 - 8x.
Solution:
Question:27
Divide 3y
4
- 3y
3
- 4y
2
- 4y by y
2
- 2y.
Solution:
Question:28
Divide 2y
5
+ 10y
4
+ 6y
3
+ y
2
+ 5y + 3 by 2y
3
+ 1.
Solution:
Question:29
Divide x
4
- 2x
3
+ 2x
2
+ x + 4 by x
2
+ x + 1.
Solution:
Question:30
Divide m
3
- 14m
2
+ 37m - 26 by m
2
- 12m +13.
Solution:
Question:31
Divide x
4
+ x
2
+ 1 by x
2
+ x + 1.
Solution:
Question:32
Divide x
5
+ x
4
+ x
3
+ x
2
+ x + 1 by x
3
+ 1.
Solution:
Question:33
Divide 14x
3
- 5x
2
+ 9x - 1 by 2x - 1 and find the quotient and remainder
Solution:
Quotient = 7x
2
+ x + 5Remainder = 4
Question:34
Divide 6x
3
- x
2
- 10x - 3 by 2x - 3 and find the quotient and remainder.
Solution:
Quotient = 3x
2
+ 4x + 1 Remainder = 0
Question:35
Divide 6x
3
+ 11x
2
- 39x - 65 by 3x
2
+ 13x + 13 and find the quotient and remainder.
Solution:
Quotient = 2x -5Remainder = 0
Question:36
Divide 30x
4
+ 11x
3
- 82x
2
- 12x + 48 by 3x
2
+ 2x - 4 and find the quotient and remainder.
Solution:
Quotient = 10x
2
-3x -12Remainder = 0
Question:37
Divide 9x
4
- 4x
2
+ 4 by 3x
2
- 4x + 2 and find the quotient and remainder.
Solution:
?
Quotient = 3x
2
+ 4x + 2 and remainder = 0.
Question:38
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
Dividend Divisor
i 14x
2
+ 13x - 15 7x - 4
ii 15z
3
- 20z
2
+ 13z - 12 3z - 6
iii 6y
5
- 28y
3
+ 3y
2
+ 30y - 9 2y
2
- 6
iv 34x - 22x
3
- 12x
4
- 10x
2
- 75 3x + 7
v 15y
4
- 16y
3
+ 9y2 -
10
3
y + 6
3y - 2
vi 4y
3
+ 8y + 8y
2
+ 7 2y
2
- y + 1
vii 6y
5
+ 4y
4
+ 4y
3
+ 7y
2
+ 27y + 6 2y
3
+ 1
Solution:
i
Quotient = 2x + 3
Remainder = -
3
Divisor = 7x -
4
Divisor ×
Quotient + Remainder = (7x -
4) (2x + 3) -
?3
= 14x
2
+ 21x -
8x -
12 -
?3
= 14x
2
+ 13x -
15
= Dividend
Thus,
Divisor ×
Quotient + Remainder = Dividend
Hence verified.
ii
Quotient = 5z
2
+
10
3
z +11Remainder = 54Divisor = 3z -6Divisor × Quotient +Remainder = 3z -6 5z
2
+
10
3
z +11 +54 = 15z
3
+10z
2
+33z -30z
2
-
Hence verified.
( ) ( )
iii
Quotient = 3y
3
-5y +
3
2
Remainder = 0
Divisor = 2y
2
-
6
Divisor ×
Quotient + Remainder =
2y
2
-6 3y
3
-5y +
3
2
+0 = 6y
5
-10y
3
+3y
2
-18y
3
+30y -9 = 6y
5
-28 y
3
+3y
2
+30y -9
= Dividend
Thus, Divisor ×
Quotient + Remainder = Dividend
Hence verified.
iv
Quotient = -
4x
3
+ 2x
2
-
8x + 30
Remainder = -
285
Divisor = 3x + 7
Divisor ×
Quotient + Remainder = (3x + 7) (-
4x
3
+ 2x
2
-
8x + 30) -
285
= -
12x
4
+ 6x
3
-
24x
2
+ 90x -
28x
3
+ 14x
2
-
56x + 210 -
?285
= -
12x
4
-
22x
3
-
10x
2
+ 34x -
75
= Dividend
Thus,
Divisor ×
Quotient + Remainder = Dividend
Hence verified.
v
Quotient = 5y
3
-2y
2
+
5
3
y
( ) ( )
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Document Description: Division of Algebraic Expressions - Exercise 8.4 for Class 8 2024 is part of Mathematics (Maths) Class 8 preparation.
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Division of Algebraic Expressions - Exercise 8.4 Free PDF Download
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