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

EXERCISE 12 A

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Q1 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper

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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 :

$10p^2+7p^{-1}-2$  [∴ $\dfrac{1}{P}=P^{-1}$]

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 :

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

No 

 

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

Sol :

No , because power is in fraction .

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

Sol :

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

(vii) 2x⁴-7x²+5x-2

Sol :

Yes, It'a a polynomial

(viii) 45

Sol :

Yes, It'a a polynomial

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

Sol :

Yes, It'a a polynomial

 

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

Sol :

No

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Q2 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper

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QUESTION 2

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

[Term : A product of a number and one or more variables with exponents.

Degree : Degree of a polynomial is defined as the highest power of the variable of its individual terms]

(i) 5x

Sol :

Here, expression contains only one term '5x'. So, it is a monomial

Degree : 1 

(ii) 17x³y²z

Sol :

Monomial because it contains one term

Degree : 6

(iii) -11-7x

Sol :

Binomial because it contains two terms

Degree : 1

 

(iv) x² + 3x + 7

Sol :

Trinomial because it contains three terms

Degree : 2

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

Sol :

Binomial because it contains two terms

Degree : 3

(vi) m-8m²+m⁴-2m²

Sol :

Polynomial because it contains more than 3 terms

Degree : 4

(vii) y⁴-3y²+19

Sol :

Trinomial because it contains three terms

Degree : 4

 

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

Sol :

Polynomial because it contains more than 3 terms

Degree : 6

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Q3 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper

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QUESTION 3

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

Sol :

 2x⁴+x³y+4x²y²-7xy³-3y⁴

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Q4 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper

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QUESTION 4

Give the degree of each of the following polynomials :

(i) 5x³ + 6x² - 3x + 20

Sol :

Degree : 3

(ii) -2x + 9

Sol :

Degree : 1

(iii) x²y³ + 5x² - 9xy

Sol :

Degree : 5

(iv) -23

Sol :

Degree : 0

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Q5 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper

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QUESTION 5

Write down the numerical as well as literal coefficients of the following monomials

(i) 2πr

Sol :

Numerical coefficient : 2π

Literal coefficient : r

(ii) 6x²y²

Sol :

Numerical coefficient : 6

Literal coefficient : x²y²

(iii) -5ab²

Sol :

Numerical coefficient : -5

Literal coefficient : ab²

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

Sol :

Numerical coefficient : $\frac{4}{3}$

Literal coefficient : abc

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