Certainly! Let's analyze the given polynomial step-by-step to find the power of the term with the coefficient 6.
The polynomial provided is:
[tex]\[ P(x) = x^3 + \frac{1}{3}x^4 + 6x + 5 \][/tex]
We are asked to find the power of [tex]\( x \)[/tex] in the term that has the coefficient 6.
Let's break down the polynomial into its individual terms:
1. [tex]\( x^3 \)[/tex] - The coefficient here is 1, and the power of [tex]\( x \)[/tex] is 3.
2. [tex]\( \frac{1}{3}x^4 \)[/tex] - The coefficient here is [tex]\( \frac{1}{3} \)[/tex], and the power of [tex]\( x \)[/tex] is 4.
3. [tex]\( 6x \)[/tex] - The coefficient here is 6, and the power of [tex]\( x \)[/tex] is 1.
4. 5 - This term is a constant, with no [tex]\( x \)[/tex] involved, hence the power of [tex]\( x \)[/tex] is 0.
We see that the term with the coefficient 6 is [tex]\( 6x \)[/tex].
In the term [tex]\( 6x \)[/tex], the variable [tex]\( x \)[/tex] has an exponent, or power, of 1.
Therefore, the power of the term with the coefficient 6 is [tex]\( \boxed{1} \)[/tex].
