Answer :
To find the degree of a polynomial, we need to identify the term with the highest exponent in the expression. The degree of a polynomial is simply the highest power of the variable present.
Let's examine the polynomial step-by-step:
[tex]\[ 7x^6 - 6x^5 + 2x^3 + x - 8 \][/tex]
1. Identify the Exponents: Look at each term and determine the exponent of the variable [tex]\(x\)[/tex]:
- [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] (which is the same as [tex]\(x^1\)[/tex]) has an exponent of 1.
- The term [tex]\(-8\)[/tex] (a constant term) has no variable, so its exponent is 0.
2. Determine the Highest Exponent: From the list above, the highest exponent is 6.
Thus, the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex] is 6.
Therefore, the correct option is:
C. 6
Let's examine the polynomial step-by-step:
[tex]\[ 7x^6 - 6x^5 + 2x^3 + x - 8 \][/tex]
1. Identify the Exponents: Look at each term and determine the exponent of the variable [tex]\(x\)[/tex]:
- [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] (which is the same as [tex]\(x^1\)[/tex]) has an exponent of 1.
- The term [tex]\(-8\)[/tex] (a constant term) has no variable, so its exponent is 0.
2. Determine the Highest Exponent: From the list above, the highest exponent is 6.
Thus, the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex] is 6.
Therefore, the correct option is:
C. 6
