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Answer :
To solve the problem, let's go through the steps to write the polynomial in standard form and then classify it by degree and number of terms.
1. Write the Polynomial in Standard Form:
The given polynomial is [tex]\(2x^3 - 4 + 7x^2\)[/tex].
To write it in standard form, we need to arrange the terms in order of descending powers of [tex]\(x\)[/tex]. The highest power of [tex]\(x\)[/tex] is 3 from the term [tex]\(2x^3\)[/tex], followed by the power 2 from [tex]\(7x^2\)[/tex], and finally, the constant term [tex]\(-4\)[/tex] with no [tex]\(x\)[/tex].
Therefore, the standard form of the polynomial is:
[tex]\[
2x^3 + 7x^2 - 4
\][/tex]
The corresponding answer from the given choices is:
- C. [tex]\(2x^3 + 7x^2 - 4\)[/tex]
2. Classify the Polynomial:
- By Degree:
The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex]. In this polynomial, the highest power is 3 (from the term [tex]\(2x^3\)[/tex]), so it is a third-degree polynomial.
- By Number of Terms:
We count the number of distinct terms in the polynomial. The terms are [tex]\(2x^3\)[/tex], [tex]\(7x^2\)[/tex], and [tex]\(-4\)[/tex]. There are 3 terms in total.
Therefore, the classification of the polynomial is:
- Degree: [tex]\(3\)[/tex] (Cubic polynomial)
- Number of Terms: [tex]\(3\)[/tex] (Trinomial)
The completed sentence for the classification is: "The polynomial is a cubic trinomial."
1. Write the Polynomial in Standard Form:
The given polynomial is [tex]\(2x^3 - 4 + 7x^2\)[/tex].
To write it in standard form, we need to arrange the terms in order of descending powers of [tex]\(x\)[/tex]. The highest power of [tex]\(x\)[/tex] is 3 from the term [tex]\(2x^3\)[/tex], followed by the power 2 from [tex]\(7x^2\)[/tex], and finally, the constant term [tex]\(-4\)[/tex] with no [tex]\(x\)[/tex].
Therefore, the standard form of the polynomial is:
[tex]\[
2x^3 + 7x^2 - 4
\][/tex]
The corresponding answer from the given choices is:
- C. [tex]\(2x^3 + 7x^2 - 4\)[/tex]
2. Classify the Polynomial:
- By Degree:
The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex]. In this polynomial, the highest power is 3 (from the term [tex]\(2x^3\)[/tex]), so it is a third-degree polynomial.
- By Number of Terms:
We count the number of distinct terms in the polynomial. The terms are [tex]\(2x^3\)[/tex], [tex]\(7x^2\)[/tex], and [tex]\(-4\)[/tex]. There are 3 terms in total.
Therefore, the classification of the polynomial is:
- Degree: [tex]\(3\)[/tex] (Cubic polynomial)
- Number of Terms: [tex]\(3\)[/tex] (Trinomial)
The completed sentence for the classification is: "The polynomial is a cubic trinomial."
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Rewritten by : Barada
