Answer :
To determine the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex], follow these steps:
1. Understand the concept of degree: The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] in the polynomial expression.
2. Identify each term in the polynomial:
- [tex]\(7x^6\)[/tex]
- [tex]\(-6x^5\)[/tex]
- [tex]\(2x^3\)[/tex]
- [tex]\(x\)[/tex] (which can also be written as [tex]\(1x^1\)[/tex])
- [tex]\(-8\)[/tex] (which is a constant term and can be considered as [tex]\(-8x^0\)[/tex])
3. Find the highest power of [tex]\(x\)[/tex]: Look at the exponents of [tex]\(x\)[/tex] in each term:
- The exponent in [tex]\(7x^6\)[/tex] is 6.
- The exponent in [tex]\(-6x^5\)[/tex] is 5.
- The exponent in [tex]\(2x^3\)[/tex] is 3.
- The exponent in [tex]\(x\)[/tex] is 1.
- The exponent in [tex]\(-8\)[/tex] is 0.
4. Determine the degree: The highest exponent found among these terms is 6. Therefore, the degree of the polynomial is 6.
So, the correct answer is:
A. 6
1. Understand the concept of degree: The degree of a polynomial is the highest power of the variable [tex]\(x\)[/tex] in the polynomial expression.
2. Identify each term in the polynomial:
- [tex]\(7x^6\)[/tex]
- [tex]\(-6x^5\)[/tex]
- [tex]\(2x^3\)[/tex]
- [tex]\(x\)[/tex] (which can also be written as [tex]\(1x^1\)[/tex])
- [tex]\(-8\)[/tex] (which is a constant term and can be considered as [tex]\(-8x^0\)[/tex])
3. Find the highest power of [tex]\(x\)[/tex]: Look at the exponents of [tex]\(x\)[/tex] in each term:
- The exponent in [tex]\(7x^6\)[/tex] is 6.
- The exponent in [tex]\(-6x^5\)[/tex] is 5.
- The exponent in [tex]\(2x^3\)[/tex] is 3.
- The exponent in [tex]\(x\)[/tex] is 1.
- The exponent in [tex]\(-8\)[/tex] is 0.
4. Determine the degree: The highest exponent found among these terms is 6. Therefore, the degree of the polynomial is 6.
So, the correct answer is:
A. 6
