Question

Which of the following are polynomials? In case of polynomial, write its degree:

$\sqrt{7}{x}^4-\sqrt{x}+2x-\frac{1}{3}$

Answer 1

Definition:

1. An expression of the form $a_0{x}^n+a_1{x}^{n-1}+a_2{x}^{n-2}+...+a_n$ where $a_0,a_1,a_2,...,a_n$ are real numbers and n is a whole number, is called a polynomial.
2. The highest power of the variable in a polynomial is called its degree.

$\sqrt{7}{x}^4-\sqrt{x}+2x-\frac{1}{3}=\sqrt{7}{x}^4-x^{\frac{1}{2}}+2x-\frac{1}{3}$

Given expression $\sqrt{7}{x}^4-\sqrt{x}+2x-\frac{1}{3}$is not in the form of $a_0{x}^n+a_1{x}^{n-1}+a_2{x}^{n-2}+...+a_n$ where $a_0,a_1,a_2,...,a_n$ are real numbers and n is a whole number.

Here, exponent of x is $\frac{1}{2}$ which is not an integer.

Thus, it is not a polynomial.