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  • Which of the following expressions are polynomials? Justify your answer (i) 8 (ii) \sqrt{3}x^{2}-2x (iii) 1-\sqrt{5x} (iv)\frac{1}{5x^{-2}}+5x+7 (v) \frac{(x-2)(x-4)}{x} (vi) \frac{x}{x+1} (vii) \frac{1}{7}a^{3}-\frac{2}{\sqrt{3}}a^{2}+4a-7

Which of the following expressions are polynomials? Justify your answer  

(i) 8

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

(iii) 1-\sqrt{5x}               

(iv) \frac{1}{5x^{-2}}+5x+7      

(v) \frac{(x-2)(x-4)}{x}       

(vi) \frac{x}{x+1}                    

(vii) \frac{1}{7}a^{3}-\frac{2}{\sqrt{3}}a^{2}+4a-7

(viii) \frac{1}{2x}         

Answers (1)

(i, ii, iv, vii)

Solution

Polynomial:- It is an expression of more than two algebraic terms, especially the sum of several  terms that contains different powers of the same variable(s)

Its degree is always a whole number.

 For example: x^{0},x+2  etc.

(i) Here 8 is a polynomial because it can also be written as 8.x^{0}  i.e., multiply by x^{0} .

(ii) \sqrt{3}x^{2}-2x  is also a polynomial having degree two.

(iii) 1-\sqrt{5x}  is not a polynomial because its exponent is in fraction.

(iv) \frac{1}{5x^{-2}}+5x+7  can be written as 5x^{2}+5x+7  and it is a polynomial having degree two.

(v) \frac{(x-2)(x-4)}{x}  is not polynomial because it has negative exponent.

(vi) \frac{1}{x+1}  is not a polynomial because it have negative exponent.

(vii) \frac{1}{7}a^{3}-\frac{2}{\sqrt{3}}a^{2}+4a-7  is a polynomial of degree three.

(viii) \frac{1}{2x}  is not a polynomial because it have negative exponent.

 

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