Answer :
To find the degree of the polynomial [tex]\( 7x^6 - 6x^5 + 2x^3 + x - 8 \)[/tex], we need to identify the highest power of the variable [tex]\( x \)[/tex] that has a non-zero coefficient.
Here's how you can determine the degree:
1. Identify the terms in the polynomial:
- [tex]\( 7x^6 \)[/tex]
- [tex]\(-6x^5 \)[/tex]
- [tex]\( 2x^3 \)[/tex]
- [tex]\( x \)[/tex] (which is the same as [tex]\( 1x^1 \)[/tex])
- [tex]\(-8 \)[/tex] (which is a constant term and has no [tex]\( x \)[/tex])
2. 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] (or [tex]\( 1x^1 \)[/tex]) is 1.
- The constant term [tex]\(-8\)[/tex] does not have an exponent of [tex]\( x \)[/tex].
3. Determine the highest exponent: Among these exponents, the highest is 6.
Therefore, the degree of the polynomial [tex]\( 7x^6 - 6x^5 + 2x^3 + x - 8 \)[/tex] is 6.
So, the correct answer is C. 6.
Here's how you can determine the degree:
1. Identify the terms in the polynomial:
- [tex]\( 7x^6 \)[/tex]
- [tex]\(-6x^5 \)[/tex]
- [tex]\( 2x^3 \)[/tex]
- [tex]\( x \)[/tex] (which is the same as [tex]\( 1x^1 \)[/tex])
- [tex]\(-8 \)[/tex] (which is a constant term and has no [tex]\( x \)[/tex])
2. 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] (or [tex]\( 1x^1 \)[/tex]) is 1.
- The constant term [tex]\(-8\)[/tex] does not have an exponent of [tex]\( x \)[/tex].
3. Determine the highest exponent: Among these exponents, the highest is 6.
Therefore, the degree of the polynomial [tex]\( 7x^6 - 6x^5 + 2x^3 + x - 8 \)[/tex] is 6.
So, the correct answer is C. 6.
