Question

Check whether $w+w^3$ and $\sqrt[3]{3w}+w^2$ are a polynomials or not?

Answer 1

$\text{All the variables of a polynomial}\text{should have whole numbers as}\text{exponents.}$

$\text{For}w+w^3,\text{the exponents of the}\text{variable w are 1, 3. Here all the}\text{exponents are whole numbers.}\text{Therefore, it is a polynomial.}$

$\text{In the expression}\sqrt[3]{3w}+w^2,\text{exponent}\text{of}w\text{is}\frac{1}{3},2\text{but}\frac{1}{3}\text{is not a whole}\text{number.}\text{Hence,}\sqrt[3]{3w}+w^2\text{is not a polynomial.}$