Question
What is the degree of f(x) = 7x (x−2)2(x+4)3 (1 point) Responses 3 3 7 7 5 5 6
Answers
GPT-4o mini
To find the degree of the polynomial \( f(x) = 7x (x−2)^2 (x+4)^3 \), we need to determine the highest power of \( x \) when all the factors are expanded.
1. The term \( 7x \) has a degree of \( 1 \) (the power of \( x \) is 1).
2. The term \( (x-2)^2 \) has a degree of \( 2 \) (the power of \( x \) is 2).
3. The term \( (x+4)^3 \) has a degree of \( 3 \) (the power of \( x \) is 3).
To find the total degree of \( f(x) \), we add the degrees of all the factors together:
\[
\text{Total degree} = 1 + 2 + 3 = 6
\]
Therefore, the degree of \( f(x) \) is \( 6 \).
The correct response is \( 6 \).
1. The term \( 7x \) has a degree of \( 1 \) (the power of \( x \) is 1).
2. The term \( (x-2)^2 \) has a degree of \( 2 \) (the power of \( x \) is 2).
3. The term \( (x+4)^3 \) has a degree of \( 3 \) (the power of \( x \) is 3).
To find the total degree of \( f(x) \), we add the degrees of all the factors together:
\[
\text{Total degree} = 1 + 2 + 3 = 6
\]
Therefore, the degree of \( f(x) \) is \( 6 \).
The correct response is \( 6 \).