Answer :
Let's analyze the polynomial provided: \( x^3 + \frac{1}{3} x^4 + 6x + 5 \).
To find the power of the term with the coefficient \( 6 \), we need to look at the polynomial term by term.
1. First term: \( x^3 \)
- The coefficient here is \( 1 \).
- The power of \( x \) in this term is \( 3 \).
2. Second term: \( \frac{1}{3} x^4 \)
- The coefficient here is \( \frac{1}{3} \).
- The power of \( x \) in this term is \( 4 \).
3. Third term: \( 6x \)
- The coefficient here is \( 6 \).
- The power of \( x \) in this term is \( 1 \) (since \( 6x \) is equivalent to \( 6x^1 \)).
4. Fourth term: \( 5 \)
- This is a constant term.
- The coefficient here is \( 5 \).
- There is no \( x \) variable in this term, so the power of \( x \) is \( 0 \) (since any number can be considered as the number times \( x^0 \)).
We are asked for the power of the term with the coefficient \( 6 \). Based on the third term \( 6x \), the power of \( x \) in this term is \( 1 \).
Therefore, the power of the term with the coefficient \( 6 \) is:
B. 1
To find the power of the term with the coefficient \( 6 \), we need to look at the polynomial term by term.
1. First term: \( x^3 \)
- The coefficient here is \( 1 \).
- The power of \( x \) in this term is \( 3 \).
2. Second term: \( \frac{1}{3} x^4 \)
- The coefficient here is \( \frac{1}{3} \).
- The power of \( x \) in this term is \( 4 \).
3. Third term: \( 6x \)
- The coefficient here is \( 6 \).
- The power of \( x \) in this term is \( 1 \) (since \( 6x \) is equivalent to \( 6x^1 \)).
4. Fourth term: \( 5 \)
- This is a constant term.
- The coefficient here is \( 5 \).
- There is no \( x \) variable in this term, so the power of \( x \) is \( 0 \) (since any number can be considered as the number times \( x^0 \)).
We are asked for the power of the term with the coefficient \( 6 \). Based on the third term \( 6x \), the power of \( x \) in this term is \( 1 \).
Therefore, the power of the term with the coefficient \( 6 \) is:
B. 1
