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
[tex]4x^4+3x^4-x^4[/tex]
We will first have to write the polynomial in standard form. To do so, we will have to simplify
[tex]\begin{gathered} 4x^4+3x^4-x^4=x^4(4+3-1) \\ =x^4(7-1) \\ =x^4(6) \\ =6x^4 \end{gathered}[/tex]
So the standard form of the polynomial is 6x⁴
Part 2
we have the polynomial as
[tex]6x^4[/tex]
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
[tex]6x^4[/tex]
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
