What is the degree of f(x)=7x(x−2)2(x+4)3

Question

?(1 point)
Responses

6
6

3
3

7
7

5

Answer 1

To find the degree of the polynomial function \( f(x) = 7x(x-2)^2(x+4)^3 \), we need to determine the degree contributed by 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 can find the total degree by adding the degrees of each factor:

\[ \text{Total degree} = 1 + 2 + 3 = 6 \]

Thus, the degree of the polynomial \( f(x) \) is \( 6 \).

So the correct response is:

6