Question

Find the degree of the polynomial \[ {x-x^3}\] ?

Answer 1

Hint: The term "polynomial" refers to an expression with two or more terms. The degree can be expressed by the order of the polynomial, but the power can be represented by a number that is raised to another number known as the exponent.

Complete step by step solution:
We have given the polynomial $x - {x^3}$
Any polynomial's degree can be defined as the variable's highest power or exponent.
We have two terms in the given expression $x - {x^3}$
We will first see the power of each term individually
\[ \Rightarrow x\] - the power of the term is one
 \[ \Rightarrow {x^3}\] - the power of the term is three
We absorbed that the highest power in the given is three.
So, the degree of the polynomial is three.
Hence, the polynomial $x - {x^3}$ is a Cubic polynomial because its highest degree is 3.

Note: Make sure you don't mix up the phrases degree and power, and use them correctly. The powers can be used to represent a long mathematical expression in a succinct form. When no power is applied to any variable, the value is one by default; similarly, when a term is written as a single variable rather than a constant term, the value is one by default, as in and are equal.