Question
what is the degree of f(x)=3x(x-3)^3 (x+4)^2
1)6
2)5
3)7
4)3
1)6
2)5
3)7
4)3
Answers
GPT-4o mini
To determine the degree of the polynomial \( f(x) = 3x(x-3)^3(x+4)^2 \), we need to analyze each term in the expression.
1. The term \( 3x \) has a degree of 1.
2. The term \( (x-3)^3 \) has a degree of 3 (since the exponent 3 applies to \( x \)).
3. The term \( (x+4)^2 \) has a degree of 2 (since the exponent 2 applies to \( x \)).
To find the degree of the entire polynomial, we add the degrees of each term together:
\[
\text{Degree of } f(x) = \text{Degree of } (3x) + \text{Degree of } (x-3)^3 + \text{Degree of } (x+4)^2
\]
\[
= 1 + 3 + 2 = 6
\]
Thus, the degree of the polynomial \( f(x) \) is \( 6 \).
The correct answer is:
1) 6
1. The term \( 3x \) has a degree of 1.
2. The term \( (x-3)^3 \) has a degree of 3 (since the exponent 3 applies to \( x \)).
3. The term \( (x+4)^2 \) has a degree of 2 (since the exponent 2 applies to \( x \)).
To find the degree of the entire polynomial, we add the degrees of each term together:
\[
\text{Degree of } f(x) = \text{Degree of } (3x) + \text{Degree of } (x-3)^3 + \text{Degree of } (x+4)^2
\]
\[
= 1 + 3 + 2 = 6
\]
Thus, the degree of the polynomial \( f(x) \) is \( 6 \).
The correct answer is:
1) 6