To determine the power of the term with the coefficient of [tex]\(6\)[/tex] in the polynomial [tex]\(x^3 + \frac{1}{3}x^4 + 6x + 5\)[/tex], follow these steps:
1. Identify the term with the coefficient [tex]\(6\)[/tex]:
Look through each term of the polynomial to find the term where the coefficient is [tex]\(6\)[/tex].
The polynomial is:
[tex]\[
x^3 + \frac{1}{3}x^4 + 6x + 5
\][/tex]
The terms are:
[tex]\[
x^3, \quad \frac{1}{3}x^4, \quad 6x, \quad 5
\][/tex]
Among these terms, the term with the coefficient [tex]\(6\)[/tex] is [tex]\(6x\)[/tex].
2. Determine the power of the identified term:
For the term [tex]\(6x\)[/tex], identify the exponent of the variable [tex]\(x\)[/tex].
The term [tex]\(6x\)[/tex] can be written as:
[tex]\[
6x^1
\][/tex]
This shows that the power of [tex]\(x\)[/tex] in this term is [tex]\(1\)[/tex].
Therefore, the power of the term with the coefficient [tex]\(6\)[/tex] is [tex]\(1\)[/tex].
So, the correct answer is:
C. [tex]\(1\)[/tex]
