Question

Determine the degree of the following polynomial.
${x^3} - 9x + 3{x^5}$

Answer 1

Hint: Polynomial can be defined as the expression which has two or more terms. The power can be represented by the number which is raised to another number which is known as the exponent whereas the degree can be represented by the order of the polynomial.

Complete step-by-step answer:
Take the given expression: ${x^3} - 9x + 3{x^5}$
Degree of any polynomial can be defined as the highest power or an exponent of its variable.
See here we have three terms,
The powers of the terms are as –
${x^3}$ - the power of the term is three
$ - 9x$ - the power of the term is one
$3{x^5}$ - the power of the term is five
Hence, from all the given powers, the highest power is five and it is known as the degree.
From the above polynomial it is clear that the degree of the polynomial is $5$
So, the correct answer is “5”.

Note: Do not get confused between the terms of the degree and the power and apply it accordingly. The long mathematical expression can be represented in the short form by using the powers. When there is no power raised to any variable then it is one by default, the same with the coefficient if the term is expressed as only variable and not constant term, the number one is by-default such as and are equal and and are equal.