Answer :
To determine the degree of the polynomial [tex]\( 7x^6 - 6x^5 + 2x^3 + x - 8 \)[/tex], follow these steps:
1. Understand the Degree of a Polynomial:
- The degree of a polynomial is defined as the highest power of the variable [tex]\( x \)[/tex] in the expression.
2. Identify Each Term's Exponent:
- Look at each term in the polynomial:
- [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]\( 1x^1 \)[/tex]) has an exponent of 1.
- The constant term [tex]\( -8 \)[/tex] is like [tex]\( -8x^0 \)[/tex] and has an exponent of 0.
3. Find the Term with the Highest Exponent:
- Out of the exponents (6, 5, 3, 1, and 0), the highest exponent is 6.
4. Determine the Degree:
- Therefore, the degree of the polynomial is 6.
The correct answer is:
D. 6
1. Understand the Degree of a Polynomial:
- The degree of a polynomial is defined as the highest power of the variable [tex]\( x \)[/tex] in the expression.
2. Identify Each Term's Exponent:
- Look at each term in the polynomial:
- [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]\( 1x^1 \)[/tex]) has an exponent of 1.
- The constant term [tex]\( -8 \)[/tex] is like [tex]\( -8x^0 \)[/tex] and has an exponent of 0.
3. Find the Term with the Highest Exponent:
- Out of the exponents (6, 5, 3, 1, and 0), the highest exponent is 6.
4. Determine the Degree:
- Therefore, the degree of the polynomial is 6.
The correct answer is:
D. 6
