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Answer :
To determine the degree of the polynomial [tex]\( 7x^6 - 6x^5 + 2x^3 + x - 8 \)[/tex], follow these steps:
1. Understand what the degree of a polynomial is: The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex] that appears in the polynomial with a non-zero coefficient.
2. Identify each term and its degree:
- The first term is [tex]\( 7x^6 \)[/tex]; it has a degree of 6.
- The second term is [tex]\( -6x^5 \)[/tex]; it has a degree of 5.
- The third term is [tex]\( 2x^3 \)[/tex]; it has a degree of 3.
- The fourth term is [tex]\( x \)[/tex] (which can be written as [tex]\( x^1 \)[/tex]); it has a degree of 1.
- The last term is [tex]\( -8 \)[/tex]; it has a degree of 0 (since it's a constant term).
3. Compare the degrees of all terms: Identify the highest degree among all terms.
- Degrees are: 6, 5, 3, 1, and 0.
4. Determine the highest degree: From the list of degrees, the highest one is 6.
Therefore, the degree of the polynomial [tex]\( 7x^6 - 6x^5 + 2x^3 + x - 8 \)[/tex] is [tex]\(\boxed{6}\)[/tex].
1. Understand what the degree of a polynomial is: The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex] that appears in the polynomial with a non-zero coefficient.
2. Identify each term and its degree:
- The first term is [tex]\( 7x^6 \)[/tex]; it has a degree of 6.
- The second term is [tex]\( -6x^5 \)[/tex]; it has a degree of 5.
- The third term is [tex]\( 2x^3 \)[/tex]; it has a degree of 3.
- The fourth term is [tex]\( x \)[/tex] (which can be written as [tex]\( x^1 \)[/tex]); it has a degree of 1.
- The last term is [tex]\( -8 \)[/tex]; it has a degree of 0 (since it's a constant term).
3. Compare the degrees of all terms: Identify the highest degree among all terms.
- Degrees are: 6, 5, 3, 1, and 0.
4. Determine the highest degree: From the list of degrees, the highest one is 6.
Therefore, the degree of the polynomial [tex]\( 7x^6 - 6x^5 + 2x^3 + x - 8 \)[/tex] is [tex]\(\boxed{6}\)[/tex].
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