EXERCISE 12 A
Q1 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper
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
Q2 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper
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
Q3 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper
QUESTION 3
Arrange the polynomial 4x2y2-7xy3+2x4-3y4+x3y in decreasing degree in x
Sol :
2x4+x3y+4x2y2-7xy3-3y4
Q4 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper
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
Q5 | Ex-12A | Class-8 | Schand Composite Mathematics | Fundamental concept and operations | Myhelper
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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