Question

Write the polynomial in standard form. Then classify the polynomial by degree and by number of terms. 4x^4+3x^4-x^4Write the polynomial in standard form. Simplify your answer.

Answer 1

Explanation.

The question gives a polynomial and asks us to classify the polynomial according to

1. In standard form

2. The degree

3. The number of terms

To do so, let us understand what a polynomial means

A polynomial is defined as an expression that is composed of variables, constants, and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication, and division.

Part 1

For the polynomial

`4x^4+3x^4-x^4`

We will first have to write the polynomial in standard form. To do so, we will have to simplify

`\begin{gathered} 4x^4+3x^4-x^4=x^4(4+3-1) \\ =x^4(7-1) \\ =x^4(6) \\ =6x^4 \end{gathered}`

So the standard form of the polynomial is 6x⁴

Part 2

we have the polynomial as

`6x^4`

We can see that the highest power is 4

Classification according to Degree.

so in our case, since we have the highest degree to be 4

Thus, the degree is 4. The name given to a polynomial with degree 4 is called Quartic

Part 3

We are to also classify according to the number of terms

The standard form of the polynomial is

`6x^4`

We can observe that it has just one term

A polynomial with one term is called monomial

A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too.

Therefore, the answer is Monomial