Question

How do you write a polynomial in standard form, then classify it by degree and number of terms $7x + 2 - 4{x^2} + 8{x^3}$?

Answer 1

In this question we should know that a polynomial in standard form is the sum/difference of terms arranged in descending degree order. Also, the highest power of polynomial expression is its degree and the number of components expression having is its terms.

Complete step by step answer:
In the above question, we know that
A polynomial in standard form is the sum/difference of terms arranged in descending degree order.
Therefore, we can write it in the standard form as $8{x^3} - 4{x^2} + 7x + 2$.
Now, we have to find the degree.
The degree of a term is the exponent of the variable (if there are multiple variables in the term it is the sum of the exponents).
The degree of a polynomial is the highest power of x in the above expression among its terms.
Therefore, its degree is $3$.
Now, the number of terms is the number of components added/subtracted when the polynomial is expressed in standard form.
In equation $8{x^3} - 4{x^2} + 7x + 2$ there are three terms adding and one term is subtracting. So there are a total of four terms.
Therefore, the given equation has $4$ terms.

Note: The degree of a polynomial is the highest power of the variable in a polynomial expression. A polynomial is defined as an expression of more than two algebraic terms, especially the sum (or difference) of several terms that contain different powers of the same or different variable(s). It is a linear combination of monomials.