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Write each of the operations below as an algebraic expression, find out which are polynomials and explain why.

i. Sum of number and it’s reciprocal 

ii. Sum of a number and its square root.

iii. Product of the sum and difference of a number and its square root.

1 Answer

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i. Let the number be x, then the reciprocal is 1/x

sum = \(x+\frac{1}{x}\)

This is not a polynomial, because here the operation of reciprocal is involved.

ii. Let the number be x, then the square root is √x

sum = x + √x

This not a polynomial because here the square root is taken.

iii. Let x be the number

(x + √x) (x – √x) = x2 – x

This is a polynomial.

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