Question

Check if the given expression is polynomial or not.
(1) $\frac{1}{x}+x^2$
(2) $2x^2-3\sqrt{x}+1$
(3) $\frac{x}{3}+5$

Answer 1

(1) For an algebraic expression to be a polynomial, the power of the variables must always be a whole number. The expression $\frac{1}{x}+x^2$ can also be written as $x^{-1}+x^2$

In the above expression, the power of the variable x is -1, which is not a whole number.
Hence, it is not a polynomial.

(2) For an algebraic expression to be a polynomial, the power of the variables must always be a whole number. The expression 2x² -$3\sqrt{x}+1$. can also be written as 2x² -$3x^{0.5}+1.$

In the above expression, the power of the variable x is 0.5, which is not a whole number.
Hence, it is not a polynomial.

(3) The expression $\frac{x}{3}+5$ can be written as $\left(\frac{1}{3}\right)x+5$ here the power of x is a whole number

Hence, it is a polynomial .