Answer :
To find the degree of a polynomial, you need to identify the highest power of the variable present in the expression. The polynomial given is:
[tex]\[ 7x^6 - 6x^5 + 2x^3 + x - 8 \][/tex]
Let's break down the polynomial to see the powers of the variable [tex]\( x \)[/tex]:
1. The first term is [tex]\( 7x^6 \)[/tex], where the power of [tex]\( x \)[/tex] is 6.
2. The second term is [tex]\( -6x^5 \)[/tex], where the power of [tex]\( x \)[/tex] is 5.
3. The third term is [tex]\( 2x^3 \)[/tex], where the power of [tex]\( x \)[/tex] is 3.
4. The fourth term is [tex]\( x \)[/tex], which can also be written as [tex]\( 1x^1 \)[/tex], so the power is 1.
5. The last term is [tex]\( -8 \)[/tex], which does not have [tex]\( x \)[/tex] and can be written as [tex]\( -8x^0 \)[/tex], so the power is 0.
Among these, the highest power of [tex]\( x \)[/tex] is 6. Therefore, the degree of the polynomial is 6.
So, the correct answer is:
C. 6
[tex]\[ 7x^6 - 6x^5 + 2x^3 + x - 8 \][/tex]
Let's break down the polynomial to see the powers of the variable [tex]\( x \)[/tex]:
1. The first term is [tex]\( 7x^6 \)[/tex], where the power of [tex]\( x \)[/tex] is 6.
2. The second term is [tex]\( -6x^5 \)[/tex], where the power of [tex]\( x \)[/tex] is 5.
3. The third term is [tex]\( 2x^3 \)[/tex], where the power of [tex]\( x \)[/tex] is 3.
4. The fourth term is [tex]\( x \)[/tex], which can also be written as [tex]\( 1x^1 \)[/tex], so the power is 1.
5. The last term is [tex]\( -8 \)[/tex], which does not have [tex]\( x \)[/tex] and can be written as [tex]\( -8x^0 \)[/tex], so the power is 0.
Among these, the highest power of [tex]\( x \)[/tex] is 6. Therefore, the degree of the polynomial is 6.
So, the correct answer is:
C. 6
