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S.chand mathematics solution class 8 chapter 12 Fundamental concept and operations

EXERCISE 12 A


QUESTION 1

Which of the following expressions are not polynomials ?

(i) \dfrac{1}{2}x^2-6x-\dfrac{1}{7}+x^3

Sol :

Yes , its a polynomial

 

(ii) 10p^2 + \dfrac{7}{p}-2

Sol :

p^2+7p^{-1}-2  [∴ \dfrac{1}{P}=P^{-1}]

No , its not a polynomial since it contains negative exponent(power)

 

(iii) 5z^3-\sqrt{7}z^2 +11

Sol :

Yes , it is a polynomial

 

(iv) \dfrac{5x-8x^2}{1+x}

Sol :

\begin{array}{c}x+1\overline{)-8x^2+5x~(}-8x\\-8x^2-8x\\\underline{+\phantom{8x^2}+\phantom{8x}}\\\phantom{-8x^2}+13x\end{array}

No

 

(v) \sqrt{3}x^{\tfrac{1}{2}}+5x^2-9x^2+7

Sol :

No

(vi) x^2+\dfrac{1}{x^2}

Sol :

No

(vii) 2x4-7x2+5x-2

Sol :

 

(viii) 45

Sol :

 

(ix) \dfrac{x}{2}+5

Sol :

 

(x) 7x^{-2}+x^{-1}+8

Sol :

No


QUESTION 2

Write monomial , binomial , trinomial or polynomial to classify each polynomial and also state their degree :

(i) 5x

Sol :

 

(ii) 17x3y2z

Sol :

 

(iii) -11-7x

Sol :

 

(iv) x2 + 3x + 7

Sol :

 

(v) -z+\sqrt{3}z^3

Sol :

 

(vi) m-8m<sup>2</sup>+m<sup>4</sup>-2m<sup>2</sup>

Sol :

 

(vii) y4-3y2+19

Sol :

 

(viii) \dfrac{1}{2}p^4-3p+5-p^6+11p^3

Sol :

 


QUESTION 3

Arrange the polynomial 4x2y2-7xy3+2x4-3y4+x3y in decreasing degree in x

Sol :

 


QUESTION 4

Give the degree of each of the following polynomials :

(i) 5x3 + 6x2 – 3x + 20

(ii) -2x + 9

(iii) x2y3 + 5x2 – 9xy

(iv) -23


QUESTION 5

Give the degree of each of the following polynomials :

(i) 2πr

(ii) 6x2y2

(iii) -5ab2

(iv) \dfrac{4}{3}abc


 


 

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