RD Sharma Solutions Class 8 Division Of Algebraic Expressions Exercise 8.3

RD Sharma Solutions Class 8 Chapter 8 Exercise 8.3

RD Sharma Class 8 Solutions Chapter 8 Ex 8.3 PDF Free Download

Divide: Question 1

x+2x2+3x4-x5  by 2x

Soln:

\(\frac{x+2x^{2}+3x^{4}-x^{5}}{2x}\)

 

= \(\frac{x}{2x}+\frac{2x^{2}}{2x}+\frac{3x^{4}}{2x}-\frac{x^{5}}{2x}\)

 

\(\frac{1}{2}+x+\frac{3x^{3}}{2}-\frac{1x^{4}}{2}\)

 

 

Question 2

y4 -3y3+\(\frac{1}{2}y^{2}\) by 3y

Soln:

\(\frac{y^{4}-3y^{3}+\frac{1y^{3}}{2}}{3y}\)

 

= \(\frac{y^{4}}{3y}-\frac{-3y^{3}}{3y}+\frac{\frac{1y^{2}}{2}}{3y}\)

 

= \(\frac{1y^{4-1}}{3}-y^{3-1}+\frac{1y^{2-1}}{6}\)

 

= \(\frac{1y^{3}}{3}-y^{2}+\frac{1y^{1}}{6}\)

 

 

Question 3

-4a3+4a2+a  by  2a

Soln:

\(\frac{-4a^{3}+4a^{2}+a}{2a}\)

 

= \(\frac{-4a^{3}}{2a}+\frac{4a^{2}}{2a}+\frac{a}{2a}\)

 

= -2a(3-1)+2a(2-1)+\(\frac{1}{2}\)

 

= -2a2+2a+\(\frac{1}{2}\)

 

 

 Question 4

-x6+2x4+4x3+2x2 by \({\sqrt{2}x^{2}}\)

Soln:

\(\frac{-x^{6}+2x^{4}+4x^{3}+2x^{2}}{\sqrt{2}x^{2}}\)

 

= \(\frac{-x^{6}}{\sqrt{2}x^{2}}+\frac{2x^{4}}{\sqrt{2}x^{2}}+\frac{4x^{3}}{\sqrt{2}x^{2}}+\frac{2x^{2}}{\sqrt{2}x^{2}}\)

 

= \(\frac{-1x}{\sqrt{6}}^{6-2}+\sqrt{2}x^{4-2}+2\sqrt{2}x^{3-2}+\sqrt{2}x^{2-2}\)

 

= \(\frac{-1x}{\sqrt{6}}^{4}+\sqrt{2}x^{2}+2\sqrt{2}x^{1}+\sqrt{2}x^{0}\)

 

= \(\frac{-1x}{\sqrt{6}}^{4}+\sqrt{2}x^{2}+2\sqrt{2}x+\sqrt{2}\)

 

 

Question 5

5z3-6z2+7z by 2z

Soln:

= \(\frac{5z^{3}-6z^{2}+7z}{2z}\)

 

= \(\frac{5z^{3}}{2z}-\frac{6z^{2}}{2z}+\frac{7z}{2z}\)

 

= \(\frac{5z^{3-1}}{2}-3z^{2-1}+\frac{7}{2}\)

 

= \(\frac{5z^{2}}{2}-3z+\frac{7}{2}\)

 

 

Question 6

\({\sqrt{3}a^{4}+2\sqrt{3}a^{3}+3a^{2}-6a}\) by 3a

Soln:

\(\frac{\sqrt{3}a^{4}+2\sqrt{3}a^{3}+3a^{2}-6a}{3a}\)

 

= \(\frac{\sqrt{3}a^{4}}{3a}+\frac{2\sqrt{3}a^{3}}{3a}+\frac{3a^{2}}{3a}-\frac{6a}{3a}\)

 

= \(\frac{1a^{4-1}}{\sqrt{3}a}+\frac{2a^{3-1}}{\sqrt{3}a}+a^{2-1}-2\)

 

= \(\frac{1a^{3}}{\sqrt{3}a}+\frac{2a^{2}}{\sqrt{3}a}+a^{1}-2\)


Practise This Question

If x and y are distinct integers, which of the following is true about x+y2?