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Answer :
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.
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.
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Rewritten by : Barada
