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Answer :
To solve this problem, let's address each part step by step.
1. Write the polynomial in standard form:
The given polynomial is [tex]\(7x^3 - 3 + 4x^2\)[/tex].
To write a polynomial in standard form, we arrange the terms in order of descending powers of [tex]\(x\)[/tex]. Therefore, the terms should be ordered from the highest degree to the lowest.
- The term [tex]\(7x^3\)[/tex] is the highest degree term.
- The next term, by degree, is [tex]\(4x^2\)[/tex].
- The constant term [tex]\(-3\)[/tex] has no [tex]\(x\)[/tex] and is therefore the lowest degree term.
Thus, the polynomial in standard form is:
[tex]\[7x^3 + 4x^2 - 3\][/tex]
2. Choose the correct answer below:
Now, let's choose the correct option that matches the standard form we just wrote:
- Option A: [tex]\(-3 + 4x^3 + 7x^3\)[/tex] (Incorrect)
- Option B: [tex]\(-3 + 7x^3 + 4x^2\)[/tex] (Incorrect)
- Option C: [tex]\(x^3 + 4x^2 - 3\)[/tex] (Incorrect)
- Option D: [tex]\(7x^3 - 3 + 4x^2\)[/tex] (Incorrect as standard form but matches the given order.
None of these options represent the standard form, but if you meant the original order, then none aligns with that either except the given order. However, standard form would be:
Correct: [tex]\(7x^3 + 4x^2 - 3\)[/tex] (for standard form order)
3. Classify the polynomial:
- By degree: The degree of a polynomial is determined by the highest power of [tex]\(x\)[/tex] in the polynomial. Here, the highest power is [tex]\(x^3\)[/tex], so this is a cubic polynomial.
- By number of terms: The polynomial has three terms: [tex]\(7x^3\)[/tex], [tex]\(4x^2\)[/tex], and [tex]\(-3\)[/tex]. A polynomial with three terms is called a trinomial.
So, the polynomial is a cubic trinomial.
1. Write the polynomial in standard form:
The given polynomial is [tex]\(7x^3 - 3 + 4x^2\)[/tex].
To write a polynomial in standard form, we arrange the terms in order of descending powers of [tex]\(x\)[/tex]. Therefore, the terms should be ordered from the highest degree to the lowest.
- The term [tex]\(7x^3\)[/tex] is the highest degree term.
- The next term, by degree, is [tex]\(4x^2\)[/tex].
- The constant term [tex]\(-3\)[/tex] has no [tex]\(x\)[/tex] and is therefore the lowest degree term.
Thus, the polynomial in standard form is:
[tex]\[7x^3 + 4x^2 - 3\][/tex]
2. Choose the correct answer below:
Now, let's choose the correct option that matches the standard form we just wrote:
- Option A: [tex]\(-3 + 4x^3 + 7x^3\)[/tex] (Incorrect)
- Option B: [tex]\(-3 + 7x^3 + 4x^2\)[/tex] (Incorrect)
- Option C: [tex]\(x^3 + 4x^2 - 3\)[/tex] (Incorrect)
- Option D: [tex]\(7x^3 - 3 + 4x^2\)[/tex] (Incorrect as standard form but matches the given order.
None of these options represent the standard form, but if you meant the original order, then none aligns with that either except the given order. However, standard form would be:
Correct: [tex]\(7x^3 + 4x^2 - 3\)[/tex] (for standard form order)
3. Classify the polynomial:
- By degree: The degree of a polynomial is determined by the highest power of [tex]\(x\)[/tex] in the polynomial. Here, the highest power is [tex]\(x^3\)[/tex], so this is a cubic polynomial.
- By number of terms: The polynomial has three terms: [tex]\(7x^3\)[/tex], [tex]\(4x^2\)[/tex], and [tex]\(-3\)[/tex]. A polynomial with three terms is called a trinomial.
So, the polynomial is a cubic trinomial.
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