Q2 of 16 Page 150

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

i) Sum of a number and its reciprocal.


ii) Sum of a number and its square root.


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

(i) Let the number be x.

So its reciprocal is



⇒


It is not a polynomial as it has a negative power of x, but for a polynomial all the powers should be positive integers.


(ii) Let the number be x.


So its square root is √x


Sum = x + √x


It is not a polynomial as it has square root which is fractional exponent, but to be a polynomial it should only have positive integer exponents.


(iii) Let sum of number and its square root be a.


⇒ a = x + √x


Let difference be b.


⇒ b = x - √x


Product of a and b.


⇒ a × b = (x + √x) × ( x - √x)


⇒ a × b = x2 – x


It’s a Polynomial as all the exponents of x are positive integer.


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