Answer :

To find the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex], you simply need to identify the highest power of the variable [tex]\(x\)[/tex] in the polynomial.

Here’s a step-by-step breakdown:

1. Identify the terms in the polynomial: The polynomial is composed of several terms: [tex]\(7x^6\)[/tex], [tex]\(-6x^5\)[/tex], [tex]\(2x^3\)[/tex], [tex]\(x\)[/tex], and [tex]\(-8\)[/tex].

2. Determine the exponent for each term:
- [tex]\(7x^6\)[/tex] has an exponent of 6.
- [tex]\(-6x^5\)[/tex] has an exponent of 5.
- [tex]\(2x^3\)[/tex] has an exponent of 3.
- [tex]\(x\)[/tex] can be written as [tex]\(x^1\)[/tex] which has an exponent of 1.
- [tex]\(-8\)[/tex] is a constant term and can be considered as [tex]\(x^0\)[/tex], with an exponent of 0.

3. Identify the highest exponent: Among the terms, the exponents are 6, 5, 3, 1, and 0. The highest exponent here is 6.

Therefore, the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex] is 6.

Answer: C. 6

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