Question

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

$\frac{2+7x^2}{8}-x^3$

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.

$\frac{2+7x^2}{8}-x^3=\frac{1}{4}+\frac{7}{8}{x}^2-x^3$

Given expression $\frac{2+7x^2}{8}-x^3$ is 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, $n=3$.

Thus, it is a polynomial.

The highest exponent is $3$.

Thus, the degree of the polynomial is $3$.