## 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**

- 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 8.2
- RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.3
- 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 8.5
- RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.6

**Question 1.
**

**Write the degree of each of the following polynomials :**

(i) 2x

(ii) 5x

(iii) 2x + x

(i) 2x

^{3}+5x^{2}-7(ii) 5x

^{2}– 3x +7 ’(iii) 2x + x

^{2}–**-8**

**(iv) \(\frac { 1 }{ 2 }\)**

**y**

(v) 3x

^{7}-12y^{5}+ 48y^{6}– 10(v) 3x

^{3}+ 1**(vi) 5**

**(vii) 20x**

^{3}+ 12x^{2}y^{2}– 10y^{2}+ 20

**Solution:**

**(i)**2x

^{3}+ 5x

^{2}-7: The degree of this polynomial is 3.

**(ii)**5x

^{2}– 3x + 2 : The degree of this polynomial is 2.

**(iii)**2x + x

^{2}– 8 : The degree of this polynomial is 2.

**(iv)**\(\frac { 1 }{ 2 }\) y

^{7}– 12y

^{6}+ 48y

^{5}– 10 : The degree of this polynomial is 7.

**(v)**3x

^{3}+ 1 : The degree of this polynomial is 3.

**(vi)**5 : The degree of this polynomial is 0 as it is only constant term

**(vii)**20x

^{3}+ 12x

^{2}y

^{2}– 10y

^{2}+ 20: The degree of this polynomial is 2 + 2 = 4.

**Question 2.
**

**Which of the following expressions are not polynomials :**

**(i) x**

^{2}+ 2x^{2}**(ii) √a x + x**

^{2}-x^{3 }(iii) 3y^{3}– √5y + 9**(iv) ax**

^{1/2 }+ ax + 9x^{2}+ 4**(v) 3x**

^{2}+ 2x^{-1}+ 4x + 5**Solution:**

**(i)**x

^{2}+ 2x

^{-2}= x

^{2}+ 2x \(\frac { 1 }{ { x }^{ 2 } }\) =x

^{2}+ \(\frac { 1 }{ { x }^{ 2 } }\)

: It is not xx polynomial as it has negative integral power.

**(ii)**√ax + x

^{2}– x

^{3}: It is polynomial.

**(iii)**3y

^{3}√5y + 9 : It is a polynomial.

**(iv)**ax

^{1/2}+ ax + 9x

^{2}+ 4: It is not a polynomial as the degree of \(\frac { 1 }{ { x }^{ 2 } }\) is an integer.

**(v)**3x

^{2}+ 2x

^{-1}+ 4x + 5 : It is not a polynomial as the degree of x

^{–}

^{2}, x

^{-1}are negative.

**Question 3.
**

**Write each of the following polynomials in the standard form. Also write their degree.**

**(i) x**

^{2}+ 3 + 6x + 5x^{4}**(ii) a**

^{1}+ 4 + 5a^{6 }(iii) (x^{3}– 1) (x^{3}– 4)**(iv) (y**

^{3}– 2) (y^{3}+ 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.

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

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