Question

State whether the given algebraic expressions are polynomials ? Justify.
$2-5\sqrt{x}$

Answer 1

A Polynomial is an algebraic expression, in which the variables have non negative integral (Whole numbers) powers.

Ex: $3x^5+4x+1$

Since, all powers of the variables are whole numbers. So it is a polynomial.

Now lets verify given algebraic expression, $2-5\sqrt{x}$

$=\text{2 - 5}{\left(x\right)}^{\frac{1}{2}}$

Here the power of the variable $x$ is $\frac{1}{2}$. {Not a whole number]

So, it is not a polynomial.