RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-1) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Created by: Abhishek Kapoor

Class 8 : RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-1) Class 8 Notes | EduRev

The document RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-1) Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
All you need of Class 8 at this link: Class 8

Question 1: Write the degree of each of the following polynomials.
(i) 2x2 + 5x2 − 7
(ii) 5x2 − 3x + 2
(iii) 2x + x2 − 8
(iv) 1/2 
y712y6+48y51012y7-12y6+48y5-10
(v) 3x3 + 1
(vi) 5
(vii) 20x3 + 12x2y2 − 10y2 + 20
Answer 1:
(i)  Correction  : It is 2x3+5x2−7  instead of 2x2+5x2−7.The degree of the polymonial  2x3+5x27 is 3.(ii) The degree of the polymonial 5x235x+2 is 2.(iii) The degree of the polymonial 2x+x28 is 2.(iv) The degree of the polymonial 12y712y6+48y510 is 7.(v) The degree of the polymonial 3x3+1 is 3.(vi) 5 is a constant polynomial and its degree is 0.(vii) The degree of the polymonial 20x3+12x2y210y2+20 is 4.Question 2: Which of the following expressions are not polynomials?
(i) x2 + 2x−2 
(ii) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-1) Class 8 Notes | EduRev+x2−x3
(iii) 3y3 −RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-1) Class 8 Notes | EduRev5y + 9 
(iv) ax1/2 + ax + 9x2 + 4
(v) 3x−2 + 2x−1 + 4x +5 

Answer 2: (i) x2+2x2 is not a polynomial because 2 is the power of variable x is not a non negative integer. 

(ii) RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-1) Class 8 Notes | EduRev+x2x3 is not a polynomial because 1/2 is the power of variable x is not a non negative integer.

(iii) 3y3−√5y+9 is a polynomial because the powers of variable y are non negative integers. 

(iv) ax1/2+ax+9x2+4 is not a polynomial because 1/2 is the power of variable x is not a non negative integer. 
(v) 3x−2+2x−1+4x+5 is not a polynomial because −2 and −1 are the powers of variable x are not non negative integers.
Question 3: Write each of the following polynomials in the standard form. Also, write their degree.
(i) x2 + 3 + 6x + 5x4
(ii) a2 + 4 + 5a6
(iii) (x3 − 1)(x3 − 4)
(iv) (y3 − 2)(y3 + 11)
(v) (a3−8/3)(a3+16/17)
(vi) (a+3/4)(a+4/3)a+34a+43

Answer 3: (i) Standard form of the given polynomial can be expressed as:(5x4+x2+6x+3) or (3+6x+x2+5x4) The degree of the polynomial is 4.(ii) Standard form of the given polynomial can be expressed as:(5a6+a2+4) or (4+a2+5a6) The degree of the polynomial is 6.(iii) (x31)(x34)=x65x3+4Standard form of the given polynomial can be expressed as:(x65x3+4) or (45x3+x6)The degree of the polynomial is 6.(iv) (y32)(y3+11)=y6+9y322Standard form of the given polynomial can be expressed as:(y6+9y322) or (22+9y3+y6)The degree of the polynomial is 6. (v) (a33/8)(a3+16/17)=a6+77/136 a36/17
Standard form of the given polynomial can be expressed as: 
(a6+77/136 a36/17) or (6/17 +77/136 a3+a6)
The degree of the polynomial is 6. 
(vi) (a+3/4)(a+4/3)=a2+25/12 a+1 
Standard form of the given polynomial can be expressed as:(a2+25/12 a+1) or (1+25/12 a+a2)The degree of the polynomial is 2.

Question 4: Divide 6x3y2z2 by 3x2yz.
Answer 4: 

RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-1) Class 8 Notes | EduRev

 = 2x(32)y(21)z(21)=2xyz 
Question 5: Divide 15m2n3 by 5m2n2.
Answer 5:

 RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-1) Class 8 Notes | EduRev
RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-1) Class 8 Notes | EduRev

=3m(22)n(32)=3m0n