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Answer :
To find the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex], follow these steps:
1. Identify the powers of [tex]\(x\)[/tex] in each term: The polynomial consists of several terms: [tex]\(7x^6\)[/tex], [tex]\(-6x^5\)[/tex], [tex]\(2x^3\)[/tex], [tex]\(x\)[/tex], [tex]\(-8\)[/tex].
- [tex]\(7x^6\)[/tex] has a power of 6.
- [tex]\(-6x^5\)[/tex] has a power of 5.
- [tex]\(2x^3\)[/tex] has a power of 3.
- [tex]\(x\)[/tex] can be written as [tex]\(1x^1\)[/tex] and has a power of 1.
- [tex]\(-8\)[/tex] is a constant term and can be written as [tex]\(-8x^0\)[/tex] with a power of 0.
2. Determine the highest power of [tex]\(x\)[/tex]: Look at all the powers of [tex]\(x\)[/tex] in the polynomial. They are 6, 5, 3, 1, and 0.
3. Identify the degree of the polynomial: The degree of a polynomial is the highest power of [tex]\(x\)[/tex] with a non-zero coefficient.
From the terms listed, the highest power is [tex]\(6\)[/tex].
Therefore, the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex] is 6.
The correct answer is:
D. 6
1. Identify the powers of [tex]\(x\)[/tex] in each term: The polynomial consists of several terms: [tex]\(7x^6\)[/tex], [tex]\(-6x^5\)[/tex], [tex]\(2x^3\)[/tex], [tex]\(x\)[/tex], [tex]\(-8\)[/tex].
- [tex]\(7x^6\)[/tex] has a power of 6.
- [tex]\(-6x^5\)[/tex] has a power of 5.
- [tex]\(2x^3\)[/tex] has a power of 3.
- [tex]\(x\)[/tex] can be written as [tex]\(1x^1\)[/tex] and has a power of 1.
- [tex]\(-8\)[/tex] is a constant term and can be written as [tex]\(-8x^0\)[/tex] with a power of 0.
2. Determine the highest power of [tex]\(x\)[/tex]: Look at all the powers of [tex]\(x\)[/tex] in the polynomial. They are 6, 5, 3, 1, and 0.
3. Identify the degree of the polynomial: The degree of a polynomial is the highest power of [tex]\(x\)[/tex] with a non-zero coefficient.
From the terms listed, the highest power is [tex]\(6\)[/tex].
Therefore, the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex] is 6.
The correct answer is:
D. 6
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