Question

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

$1+5x-2x^2-\frac{1}{6}{x}^3$

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.

Given expression $1+5x-2x^2-\frac{1}{6}{x}^3$ 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.