Question
Jaime was asked to construct a polynomial function with the following
zeros and multiplicities. Which function should he write?
Zero Multiplicity
1
3
(1 point)
x = 4
x = −2
f (x) = (x − 4)(x + 2)
3
f (x) = (x + 4)(x − 2)
f (x) = (x − 4)(x + 2)
f (x) = (x + 4)(x − 2)
3
zeros and multiplicities. Which function should he write?
Zero Multiplicity
1
3
(1 point)
x = 4
x = −2
f (x) = (x − 4)(x + 2)
3
f (x) = (x + 4)(x − 2)
f (x) = (x − 4)(x + 2)
f (x) = (x + 4)(x − 2)
3
Answers
GPT-4o mini
To construct a polynomial function with given zeros and multiplicities, we need to follow these instructions:
1. Identify the zeros and their corresponding multiplicities.
2. Write the factors corresponding to each zero, raised to the power of their multiplicity.
From the question, we need to clarify the provided zeros and their multiplicities. You indicated the following:
- Zero: \( x = 4 \) with a multiplicity of 3
- Zero: \( x = -2 \) with a multiplicity of 1
Using this information, the polynomial can be constructed as follows:
- For the zero \( x = 4 \) with multiplicity 3, the factor is \( (x - 4)^3 \).
- For the zero \( x = -2 \) with multiplicity 1, the factor is \( (x + 2) \).
Putting it all together, the polynomial function \( f(x) \) will be:
\[
f(x) = (x - 4)^3 (x + 2)
\]
If looking for one of the options listed, it appears none of the provided choices match exactly what we constructed since they repeat:
- **Option**: \( f(x) = (x - 4)(x + 2) \) \( \text{(not a valid polynomial; incorrect multiplicity)} \)
- **Option**: \( f(x) = (x + 4)(x - 2) \) \( \text{(totally different zeros)} \)
Thus, the correct function based on the information given that matches the requirement for \( x = 4 \) (multiplicity of 3) and \( x = -2 \) (multiplicity of 1) isn't among the options you've provided.
The correct polynomial is:
\[
f(x) = (x - 4)^3 (x + 2)
\]
Make sure to double-check the provided options. If the zeroes and their multiplicities have been quoted correctly, none of the provided choices fit.
1. Identify the zeros and their corresponding multiplicities.
2. Write the factors corresponding to each zero, raised to the power of their multiplicity.
From the question, we need to clarify the provided zeros and their multiplicities. You indicated the following:
- Zero: \( x = 4 \) with a multiplicity of 3
- Zero: \( x = -2 \) with a multiplicity of 1
Using this information, the polynomial can be constructed as follows:
- For the zero \( x = 4 \) with multiplicity 3, the factor is \( (x - 4)^3 \).
- For the zero \( x = -2 \) with multiplicity 1, the factor is \( (x + 2) \).
Putting it all together, the polynomial function \( f(x) \) will be:
\[
f(x) = (x - 4)^3 (x + 2)
\]
If looking for one of the options listed, it appears none of the provided choices match exactly what we constructed since they repeat:
- **Option**: \( f(x) = (x - 4)(x + 2) \) \( \text{(not a valid polynomial; incorrect multiplicity)} \)
- **Option**: \( f(x) = (x + 4)(x - 2) \) \( \text{(totally different zeros)} \)
Thus, the correct function based on the information given that matches the requirement for \( x = 4 \) (multiplicity of 3) and \( x = -2 \) (multiplicity of 1) isn't among the options you've provided.
The correct polynomial is:
\[
f(x) = (x - 4)^3 (x + 2)
\]
Make sure to double-check the provided options. If the zeroes and their multiplicities have been quoted correctly, none of the provided choices fit.