Question
What is the degree of f(x)=7x(x−2)2(x+4)3
?(1 point)
Responses
5
5
3
3
7
7
6
?(1 point)
Responses
5
5
3
3
7
7
6
Answers
GPT-4o mini
To determine the degree of the polynomial \( f(x) = 7x(x-2)^2(x+4)^3 \), we can find the degree of each factor:
1. The term \( 7x \) has a degree of 1.
2. The term \( (x-2)^2 \) has a degree of 2.
3. The term \( (x+4)^3 \) has a degree of 3.
Now we add the degrees of these factors together to find the total degree of the polynomial:
\[
\text{Degree of } f(x) = 1 + 2 + 3 = 6
\]
Thus, the degree of \( f(x) \) is 6.
The correct response is:
**6**
1. The term \( 7x \) has a degree of 1.
2. The term \( (x-2)^2 \) has a degree of 2.
3. The term \( (x+4)^3 \) has a degree of 3.
Now we add the degrees of these factors together to find the total degree of the polynomial:
\[
\text{Degree of } f(x) = 1 + 2 + 3 = 6
\]
Thus, the degree of \( f(x) \) is 6.
The correct response is:
**6**