Answer :
Sure! Let's find the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex].
1. Identify the Terms: The polynomial given is [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex]. Each part separated by a plus or minus sign is a term.
2. Check the Exponents: Look at the exponents of [tex]\(x\)[/tex] in each of the terms:
- [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] is the same as [tex]\(x^1\)[/tex] and has an exponent of 1.
- The constant [tex]\(-8\)[/tex] can be thought of as [tex]\(x^0\)[/tex], which has an exponent of 0.
3. Determine the Highest Exponent: The degree of a polynomial is the highest exponent of [tex]\(x\)[/tex] with a non-zero coefficient. In this polynomial, the highest exponent is 6, from the term [tex]\(7x^6\)[/tex].
Therefore, the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex] is [tex]\(\boxed{6}\)[/tex].
1. Identify the Terms: The polynomial given is [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex]. Each part separated by a plus or minus sign is a term.
2. Check the Exponents: Look at the exponents of [tex]\(x\)[/tex] in each of the terms:
- [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] is the same as [tex]\(x^1\)[/tex] and has an exponent of 1.
- The constant [tex]\(-8\)[/tex] can be thought of as [tex]\(x^0\)[/tex], which has an exponent of 0.
3. Determine the Highest Exponent: The degree of a polynomial is the highest exponent of [tex]\(x\)[/tex] with a non-zero coefficient. In this polynomial, the highest exponent is 6, from the term [tex]\(7x^6\)[/tex].
Therefore, the degree of the polynomial [tex]\(7x^6 - 6x^5 + 2x^3 + x - 8\)[/tex] is [tex]\(\boxed{6}\)[/tex].
