RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4

RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4

Other Exercises

Question 1.
5x3 – 15x2 + 25x by 5x
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 1

Question 2.
4z3 + 6z2-zby \(\frac { -1 }{ 2 }\) z
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 2

Question 3.
9x2y – 6xy + 12xy2 by \(\frac { -3 }{ 2 }\) xy
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 3
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 4

Question 4.
3x2y2 + 2x2y + 15xy by 3xy
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 5

Question 5.
x2 + 7x + 12 by x + 4
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 6

Question 6.
4y4 + 3y + \(\frac { -1 }{ 2 }\) by 2y + 1
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 7
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 8

Question 7.
3x3 + 4x2 + 5x + 18 by x + 2
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 9

Question 8.
14x2 – 53x + 45 by 7a – 9
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 10

Question 9.
-21 + 71x – 31x2 – 24ax3 by 3 – 8ax
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 11
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 12

Question 10.
3y4 – 3y3 – 4y2 – 4y by y2 – 2y
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 13

Question 11.
2y5 + 10y4 + 6y3 + y2 + 5y + 3 by 2y3 + 1
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 14
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 15

Question 12.
x4 – 2x3 + 2x2 + x + 4 by x2 + x + 1
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 16

Question 13.
m3 – 14m2 + 37m – 26 by m2 – 12m + 13
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 17

Question 14.
x4 + x2 + 1 by x2 + x + 1
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 18
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 19

Question 15.
x5 + x4 + x3+x2 + x+ 1 by x3 + 1
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 20

Divide each of the following and find the quotient and remainder :

Question 16.
14x3 – 5x2 + 9x -1 by 2x – 1
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 21

Question 17.
6x3 – x2 – 10x – 3 by 2x – 3
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 22
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 23

Question 18.
6x3+ 11x2 – 39x – 65 by 3x2 + 13x + 13
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 24

Question 19.
30a4 + 11a3-82a2– 12a + 48 by 3a2 + 2a- 4
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 25

Question 20.
9x4 – 4x2 + 4 by 3x2 – 4x + 2
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 26

Question 21.
Verify division algorithm i.e., Dividend = Divisor * Quotient + Remainder, in each of the following. Also, write the quotient and remainder :
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 27
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 28
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 29
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 30
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 31
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 32
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 33

Question 22.
Divide 15y4 + 16y3 + \(\frac { 10 }{ 3 }\) y – 9y2 – 6 by 3y – 2
Write down the co-efficients of the terms in the quotient.
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 34
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 35

Question 23.
Using division of polynomials state whether.
(i) x + 6 is a factor of x2 – x – 42
(ii) 4x – 1 is a factor of 4x2 – 13x – 12
(iii) 2y – 5 is a factor of 4y4 – 10y3 – 10y2 + 30y -15
(iv) 3y + 5 is a factor of 6y5 + 15y + 16y + 4y+ 10y – 35
(v) z2 + 3 is a factor of z5– 9z
(vi) 2x2 – x + 3 is a factor of 60x5-x4 + 4x3 – 5x2 -x- 15
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 36
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 37
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 38
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 39
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 40
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 41

Question 24.
Find the value of ‘a’, if x + 2 is a factor of 4x4 + 2x3 – 3x2 + 8x + 5a.
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 42
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 43

Question 25.
What must be added to x4 + 2x3 — 2x2 + x – 1 so that the resulting polynomial is exactly divisible by x2 + 2x – 3.
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 44

Hope given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.4 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6

RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6

Other Exercises

Factorize each of the following algebraic expressions :
Question 1.
4x2 + 12xy + 9y2
Solution:
4x2 + 12xy + 9y2 = (2x)2 + 2 x 2x x 3y + (3y)2 {∵ a2 + 2ab + b2 = (a +b)2}
= (2x + 3y)2    

Question 2.
9a2 – 24ab + 16b2
Solution:
9a2 – 24ab + 16b2
= (3a)2 – 2 x 3a x 4b + (4b)2     {∵ a2 – 2ab + b2 = (a – b)2}
= (3a – 4b)2

Question 3.
36a2 – 6pqr + 9r2
Solution:
p2q2 – 6pqr + 9r2
= (pq)2 – 2 x pq x3r + (3r){∵ a2 – 2ab + b2 = (a -b)2}
= (pq-3r)2

Question 4.
36a2 + 36a + 9
Solution:
36a2 + 36a + 9
= (6a)2 + 2 x 6a x 3 + (3)2   {∵ a2 + 2ab + b2 = (a + b)2
= (6a + 3)2

Question 5.
a2 + 2ab + b2 – 16
Solution:
a2 + 2ab + b2 – 16
= (a + b)2 – (4)2     {∵ a2 + 2ab + b2 = (a + b)2 and a2 – b2 = (a + b) (a – b)}
= (a + b + 4) (a + b – 4)

Question 6.
9z2 – x2 + 4xy – 4y2
Solution:
9z2 – x2 + 4xy – 4y2    {∵ a2 – b2 = (a + b) (a – b) and a2 – 2ab + b2 (a – b)2}
= 9z2 – (x2 – 4xy + 4y2)
= (3z)2 – [(x)2 – 2 x x x 2y + (2y)2]
= (3z)2-(x-2y)2
= (3z + x – 2y) (3z – x + 2y)

Question 7.
9a4 – 24a2b2 + 16b4 – 256
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 1

Question 8.
16 – a6 + 4a3b3 – 4b6
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 2

Question 9.
a2 – 2ab + b2 – c2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 3

Question 10.
x2 + 2x + 1 – 9y2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 4

Question 11.
a2 + 4ab + 3b2
Solution:
a2 + 4ab + 3b2
= a2 + 4ab+ 4b2 – b2
= (a)2 + 2 x a x 2b + (2b)2 – b(∵ 3b2 = 4b2 – b2)
= (a + 2b)2 – (b)2   {∵ a2 – b2 = (a +b) (a – b)}
= (a + 2b + b) (a + 2b- b)

Question 12.
96 – 4x-x2
Solution:
96 – 4x – x2 = 96 – (4x + x2)
= 96 – [(x)2 + 2 x x x 2 + (2)2] + (2)2   (on completing the square)
= 96 + 4 – (x + 2)2 = 100 – (x + 2)2
= (10)2 – (x + 2)2
= (10 + x + 2) (10 – x- 2)
= (x + 12) (-x + 8)

Question 13.
a4 + 3a2 + 4
Solution:
a4 + 3a2 + 4
= (a2)2 + (2)2 + 2 x a2 x 2 – a2   (on completing the square)
= (a2 + 2)2 – (a)2
= (a2 + 2 + a) (a2 + 2 – a)
= (a1 + a + 2) (a2 – a + 2)

Question 14.
4a4 + 1
Solution:
4x4 + 1 = (2a2)2 + (1)2 + 2 x 2x2 x 1 – 2 x 2xx 1  (completing the square)
= (2x2 + 1)2 – 4a2
= (2x2 + 1)2 – (2a)2   {a2 – b2 = (a + b) (a – b)}
= (2x2 + 1 + 2a) (2a2 + 1 – 2a)
= (2a2 + 2a + 1) (2a2 – 2a + 1)

Question 15.
4x4+y4
Solution:
4a4 + y4 = (2x2)2 + (y2)2 + 2 x 2x2y2 – 2 x 2x2y2
= (2x2 + y2)2 – 4x2y2
= (2x2 + y2)2 – (2xy)2
= (2x2 + y2 + 2xy) (2x2 + y2 – 2xy)
= (2x2 + 2xy + y2) (2x2 – 2xy + y2)

Question 16.
(x+ 2)2 – 6 (a + 2) + 9
Solution:
(x + 2)2 – 6 (x + 2) + 9
=  (x + 2)2 – 2 x (x + 2) x 3 + (3)2
= (x + 2 – 3)2
= (x-1)2 = (x-1)(x-1)

Question 17.
25 – p2 – q2 – 2pq
Solution:

RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 5

Question 18.
a2 + 9y2 – 6xy – 25a2
Solution:
a2 + 9y2 – 6xy – 25a2
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 6

Question 19.
49 – a2 + 8ab – 16b2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 7

Question 20.
a2 – 8ab + 16b2 – 25c2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 8

Question 21.
x2 -y2+ 6y- 9
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 9

Question 22.
25x2 – 10x + 1 – 36y2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 10
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 11

Question 23.
a2-b2 + 2bc – c2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 12

Question 24.
a2 + 2ab + b2 -c2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 13

Question 25.
49 -x2 – y2 + 2xy
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 14
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 15

Question 26.
a2 + 4b24ab 4c2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 16

Question 27.
x2 -y24xz + 4z2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 17

Hope given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.6 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2

RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2

Other Exercises

Divide :

Question 1.
6x3y2z2 by 3x2yz
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 1

Question 2.
15m2nby 5m2n2
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 2
Question 3.
24a3bby -8ab
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 3
Question 4.
-21abc2 by 7abc
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 4
Question 5.
72xyz2 by – 9xz
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 5
Question 6.
-72a4b5cby – 9a2b2c3
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 6

Simplify :

Question 7.
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 7
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 8
Question 8.
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 9
Solution:
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 10

Hope given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.2 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1

RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1

Other Exercises

Question 1.
Write the degree of each of the following polynomials :
(i) 2x3+5x2-7
(ii) 5x2
3x +7 ’
(iii) 2x + x2
-8
(iv) \(\frac { 1 }{ 2 }\) 
y7 -12y5 + 48y6 – 10
(v) 3x3 + 1

(vi) 5
(vii) 20x3 + 12x2y2– 10y2 + 20
Solution:
(i) 2x3 + 5x2-7: The degree of this polynomial is 3.
(ii) 5x2 – 3x + 2 : The degree of this polynomial is 2.
(iii) 2x + x2 – 8 : The degree of this polynomial is 2.
(iv) \(\frac { 1 }{ 2 }\) y7 – 12y6 + 48y5 – 10 : The degree of this polynomial is 7.
(v) 3x3 + 1 : The degree of this polynomial is 3.
(vi) 5 : The degree of this polynomial is 0 as it is only constant term
(vii) 20x3 + 12x2y2 – 10y2 + 20: The degree of this polynomial is 2 + 2 = 4.

Question 2.
Which of the following expressions are not polynomials :
(i) x2 + 2x2                   
(ii) √a x + x2-x3
(iii) 3y3 – √5y + 9      

(iv) ax1/2 + ax + 9x2 + 4
(v) 3x2 + 2x-1 + 4x + 5
Solution:
(i) x2 + 2x-2 = x2 + 2x \(\frac { 1 }{ { x }^{ 2 } }\) =x2 + \(\frac { 1 }{ { x }^{ 2 } }\)
: It is not xx polynomial as it has negative integral power.
(ii) √ax + x2 – x3: It is polynomial.
(iii) 3y3  √5y + 9 : It is a polynomial.
(iv) ax1/2+ ax + 9x2 + 4: It is not a polynomial as  the degree of \(\frac { 1 }{ { x }^{ 2 } }\) is an integer.
(v) 3x2 + 2x-1 + 4x + 5 : It is not a polynomial as the degree of x2, x-1 are negative.

Question 3.
Write each of the following polynomials in the standard form. Also write their degree.
(i) x2 + 3 + 6x + 5x4
(ii) a1 + 4 + 5a6
(iii) (x3 – 1) (x3 – 4)

(iv) (y3 – 2) (y3 + 11)
(v) \(\left( { a }^{ 3 }-\frac { 3 }{ 8 } \right)\) \(\left( { a }^{ 3 }-\frac { 16 }{ 17 } \right)\)
(vi) \(\left( { a }+\frac { 3 }{ 4 } \right)\) \(\left( { a }+\frac { 3 }{ 4 } \right)\)
Solution:
Polynomial in standard form is the polynomial in ascending order or descending order.
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1 1

Hope given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7

RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7

Other Exercises

Factorize each of the following algebraic expressions :
Question 1.
x2 + 12x – 45
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 1
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 2

Question 2.
40 + 3x – x2
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 3
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 3.1

Question 3.
a2 + 3a-88
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 4

Question 4.
a2 – 14a – 51
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 5

Question 5.
x2 + 14x + 45
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 6

Question 6.
x2 – 22x + 120
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 7

Question 7.
x2– 11x – 42
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 8
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 9

Question 8.
a2 + 2a – 3
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 10

Question 9.
a2 + 14a + 48
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 11

Question 10.
x2 – 4x – 21
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 12

Question 11.
y2 – 5y-36
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 13

Question 12.
(a2-5a)2-36
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 14
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 15

Question 13.
(a + 7) (a – 10) + 16
Solution:
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 16
RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 17

Hope given RD Sharma Class 8 Solutions Chapter 7 Factorizations Ex 7.7 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.