Question
What is the degree of f(x)=7x(x−2)2(x+4)3
?(1 point)
Responses
7
7
6
6
5
5
4
?(1 point)
Responses
7
7
6
6
5
5
4
Answers
GPT-4o mini
To find the degree of the polynomial function \( f(x) = 7x(x-2)^2(x+4)^3 \), we can determine the degree by analyzing the degree of each factor.
1. The factor \( 7x \) has a degree of 1.
2. The factor \( (x-2)^2 \) has a degree of 2.
3. The factor \( (x+4)^3 \) has a degree of 3.
Now, we sum the degrees of all the factors:
\[
\text{Total degree} = 1 + 2 + 3 = 6
\]
Therefore, the degree of \( f(x) \) is \( 6 \).
The correct response is:
**6**
1. The factor \( 7x \) has a degree of 1.
2. The factor \( (x-2)^2 \) has a degree of 2.
3. The factor \( (x+4)^3 \) has a degree of 3.
Now, we sum the degrees of all the factors:
\[
\text{Total degree} = 1 + 2 + 3 = 6
\]
Therefore, the degree of \( f(x) \) is \( 6 \).
The correct response is:
**6**