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Answer :
Sure, let's break down the problem step-by-step to identify the first-degree term in the polynomial expression.
The polynomial expression given is:
[tex]\[
-3x^7 + 9x^5 - 4x^3 - 6x + 1
\][/tex]
This is a polynomial consisting of several terms, each with a different degree. The degree of a term is determined by the exponent of [tex]\(x\)[/tex]. We are interested in finding the first-degree term of this polynomial.
Steps to identify the first-degree term:
1. Identify the degree of each term:
- [tex]\(-3x^7\)[/tex] is a 7th-degree term because the exponent of [tex]\(x\)[/tex] is 7.
- [tex]\(9x^5\)[/tex] is a 5th-degree term because the exponent of [tex]\(x\)[/tex] is 5.
- [tex]\(-4x^3\)[/tex] is a 3rd-degree term because the exponent of [tex]\(x\)[/tex] is 3.
- [tex]\(-6x\)[/tex] is a 1st-degree term because the exponent of [tex]\(x\)[/tex] is 1.
- [tex]\(1\)[/tex] is a constant term and is considered a 0th-degree term because it can be thought of as [tex]\(1 \times x^0\)[/tex].
2. Identify the first-degree term:
- From the list above, we can see that the term [tex]\(-6x\)[/tex] has an exponent of 1. Therefore, it is the first-degree term in the polynomial.
3. Find the coefficient of the first-degree term:
- The coefficient of the first-degree term [tex]\(-6x\)[/tex] is [tex]\(-6\)[/tex].
So, the coefficient of the first-degree term in the polynomial expression is [tex]\(-6\)[/tex].
The polynomial expression given is:
[tex]\[
-3x^7 + 9x^5 - 4x^3 - 6x + 1
\][/tex]
This is a polynomial consisting of several terms, each with a different degree. The degree of a term is determined by the exponent of [tex]\(x\)[/tex]. We are interested in finding the first-degree term of this polynomial.
Steps to identify the first-degree term:
1. Identify the degree of each term:
- [tex]\(-3x^7\)[/tex] is a 7th-degree term because the exponent of [tex]\(x\)[/tex] is 7.
- [tex]\(9x^5\)[/tex] is a 5th-degree term because the exponent of [tex]\(x\)[/tex] is 5.
- [tex]\(-4x^3\)[/tex] is a 3rd-degree term because the exponent of [tex]\(x\)[/tex] is 3.
- [tex]\(-6x\)[/tex] is a 1st-degree term because the exponent of [tex]\(x\)[/tex] is 1.
- [tex]\(1\)[/tex] is a constant term and is considered a 0th-degree term because it can be thought of as [tex]\(1 \times x^0\)[/tex].
2. Identify the first-degree term:
- From the list above, we can see that the term [tex]\(-6x\)[/tex] has an exponent of 1. Therefore, it is the first-degree term in the polynomial.
3. Find the coefficient of the first-degree term:
- The coefficient of the first-degree term [tex]\(-6x\)[/tex] is [tex]\(-6\)[/tex].
So, the coefficient of the first-degree term in the polynomial expression is [tex]\(-6\)[/tex].
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