RD Sharma Solutions for Class 8 Math Chapter 8 - Division of Algebraic Expressions (Part-1) | RD Sharma Solutions for Class 8 Mathematics PDF Download

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 y7−12y6+48y5−1012y7-12y6+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+5x2−7 is 3.(ii) The degree of the polymonial 5x2−35x+2 is 2.(iii) The degree of the polymonial 2x+x2−8 is 2.(iv) The degree of the polymonial 12y7−12y6+48y5−10 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+12x2y2−10y2+20 is 4.Question 2: Which of the following expressions are not polynomials?
(i) x² + 2x⁻² 
(ii) +x²−x^{3
(iii) 3y3 −5y + 9 
(iv) ax1/2 + ax + 9x2 + 4
(v) 3x−2 + 2x−1 + 4x +5} 
Answer 2: (i) x2+2x−2 is not a polynomial because −2 is the power of variable x is not a non negative integer. 
(ii) +x2−x3 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) ax^1/2+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) (x3−1)(x3−4)=x6−5x3+4Standard form of the given polynomial can be expressed as:(x6−5x3+4) or (4−5x3+x6)The degree of the polynomial is 6.(iv) (y3−2)(y3+11)=y6+9y3−22Standard form of the given polynomial can be expressed as:(y6+9y3−22) or (−22+9y3+y6)The degree of the polynomial is 6. (v) (a3−3/8)(a3+16/17)=a6+77/136 a3−6/17
Standard form of the given polynomial can be expressed as: 
(a6+77/136 a3−6/17) 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: 

 = 2x(3−2)y(2−1)z(2−1)=2xyz 
Question 5: Divide 15m²n³ by 5m²n².
Answer 5:

=3m(2−2)n(3−2)=3m0n1=3n

Question 6: Divide 24a³b³ by −8ab.
Answer 6:

 

=−3a(3−1)b(3−1)=−3a2b2Question 7: Divide −21abc² by 7abc.
Answer 7: 

=−3a(1−1)b(1−1)c(2−1)=−3c 
Question 8: Divide 72xyz² by −9xz.
Answer 8:

 

=−8x(1−1)yz(2−1)=−8yzQuestion 9: Divide −72a⁴b⁵c⁸ by −9a²b²c³.
Answer 9:

 

=8a(4−2)b(5−2)c(8−3)=8a2b3c5Question 10: Simplify:

Answer 10: 

=4m(3−2)y(2−1)=4my Question 11: Simplify:
 
Answer 11:

 

=8m(2−1)n(3−1)p(2−1)=8mn2pQuestion 12: Divide x + 2x² + 3x⁴ − x⁵ by 2x.
Answer 12: 

Question 13: Divide y4−3y3+1/2 y2 by 3yy4-3y3+12y2 by 3y. 
Answer 13:  

Question 14: Divide −4a³ + 4a² + a by 2a.

Answer 14: 

=−2a2+2a+1/2
Question 15: Divide −x6+2x4+4x3+2x2 by .
Answer 15: 

Question 16: Divide 5z³ − 6z² + 7z by 2z.
Answer 16:

 



Question 17: Divide +3a²−6a by 3a.
Answer 17: