Write the polynomial in standard form. Then classify it by degree and by number of terms.

Given: [tex]2x^3 - 4 + 7x^2[/tex]

Write the polynomial in standard form. Choose the correct answer below.

A. [tex]-4 + 2x^3 + 7x^2[/tex]
B. [tex]-4 + 7x^2 + 2x^3[/tex]
C. [tex]2x^3 + 7x^2 - 4[/tex]
D. [tex]2x^3 - 4 + 7x^2[/tex]

To write the polynomial [tex]$2x^3 - 4 + 7x^2$[/tex] in standard form, we must arrange its terms by the degree in descending order. The degree of a term in a polynomial is the exponent of its variable. Let's break down the process:

1. Identify the Terms:
- [tex]$2x^3$[/tex] has a degree of 3.
- [tex]$7x^2$[/tex] has a degree of 2.
- [tex]$-4$[/tex] is a constant term, which is considered to have a degree of 0.

2. Order the Terms:
Arrange the terms from the highest degree to the lowest degree:
- The term with the highest degree is [tex]$2x^3$[/tex].
- Next comes [tex]$7x^2$[/tex].
- Finally, the constant term [tex]$-4$[/tex].

3. Write in Standard Form:
The polynomial in standard form is [tex]$2x^3 + 7x^2 - 4$[/tex].

4. Classify the Polynomial:
- By Degree: The highest degree among the terms is 3 (from the term [tex]$2x^3$[/tex]), so this is a cubic polynomial.
- By Number of Terms: There are three terms: [tex]$2x^3$[/tex], [tex]$7x^2$[/tex], and [tex]$-4$[/tex]. Therefore, it's a trinomial.

5. Choose the Correct Answer:
From the given options, the standard form of the polynomial is option C: [tex]$2x^3 + 7x^2 - 4$[/tex].

So, the polynomial in standard form is [tex]$2x^3 + 7x^2 - 4$[/tex]. It is a cubic trinomial. The correct choice is C.