RD Sharma Solutions Class 8 Division Of Algebraic Expressions Exercise 8.1

RD Sharma Class 8 Solutions Chapter 8 Ex 8.1 PDF Free Download

RD Sharma Solutions Class 8 Chapter 8 Exercise 8.1

Question 1: Write the degree of each of the following polynomials:

Soln:

(i) 2x³+5x2-7

It is 2x³+5x2-7 instead of 2x2+5x2-7

The degree of the polynomial 2x³+5x2-7 is 3

(ii) 5x2-35x+2

The degree of the polynomial 5x2-35x+2 is 2

(iii) 2x+x2-8

The degree of the polynomial 2x+x2-8 is 2

(iv) \(\frac{1}{2}y^{7}-12y^{6}+48y^{5}-10\)

The degree of the polynomial \(\frac{1}{2}y^{7}-12y^{6}+48y^{5}-10\) is 7

(v) 3x3+1

The degree of the polynomial 3x3+1 is 3

(vi) 5

5 is a constant polynomial and its degree is 0.

(vii) 20x3+12x2y2-10y2+20

The degree of the polynomial 20x3+12x2y2-10y2+20 is 4

Question 2

Which of the following expressions are not polynomials:

Soln:

(i) x2+2x-2

x2+2x-2is not a polynomial because -2 is the power of variable x is not a non negative integer.

(ii) \(\sqrt{ax}+x^{2}-x^{3}\)

\(\sqrt{ax}+x^{2}-x^{3}\) is not a polynomial because \(\frac{1}{2}\) is the power of variable x is not a non negative integer.

(iii) \(3y^{3}-\sqrt{5}y+9\)

\(3y^{3}-\sqrt{5}y+9\) is a polynomial because the powers of variable y are non negative integers.

(iv) \(ax^{\frac{1}{2}}+ax+9x^{2}+4\)

\(ax^{\frac{1}{2}}+ax+9x^{2}+4\) is not a polynomial because \(\frac{1}{2}\) is the power of variable x is not a non negative integer.

(v) 3x-2+2x-1+4x+5

3x-2+2x-1+4x+5 is not a polynomial because -2 and -1 are the powers of variable x are not non negative integers.

Question 3

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

Soln:

(i) (x2+3+6x+5x4)

The standard form of the given polynomial can be expressed as:

(5x4+x2+6x+3) or (3+6x+x2+5x4)

The degree of the polynomial is 4

(ii) a2+4+5a6

The standard form of the given polynomial can be expressed as:

(5a6+a2+4) or (4+a2+5a6)

The degree of the polynomial is 6

(iii) (x3-1)(x3-4)

(x3-1)(x3-4) = x6-5x3+4

The standard form of the given polynomial can be expressed as:

(x6-5x3+4) or (4-5x3+x6)

The degree of the polynomial is 6

(iv) (y3-2)(y3+11)

(y3-2)(y3+11) = y6+9y3-22

The standard form of the given polynomial can be expressed as:

(y6+9y3-22) or (-22+9y3+y6)

The degree of the polynomial is 6

(v) \((a^{3}-\frac{3}{8})(a^{3}+\frac{16}{17}) (a^{3}-\frac{3}{8})(a^{3}+\frac{16}{17})=a^{3}+\frac{77}{136}a^{3}-\frac{6}{17}\)

Standard form of the given polynomial can be expressed as:

(\(a^{3}+\frac{77}{136}a^{3}-\frac{6}{17}\))  or (\(-\frac{6}{17}+\frac{77}{136}a^{3}+ a^{3} \))

The degree of the polynomial is 6.

(vi) \((a+\frac{3}{4})(a+\frac{4}{3})(a+\frac{3}{4})(a+\frac{4}{3})=a^{2}+\frac{25}{12}a+1\)

Standard form of the given polynomial can be expressed as:

(\(a^{2}+\frac{25}{12}a+1\))  or (\(1+\frac{25}{12}a+ a^{2} \)))

The degree of the polynomial is 2

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