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Sagot :
To answer this question, let's analyze the provided functions based on their degrees and leading coefficients. We'll match each function to its correct description:
1. [tex]\( f(x)=(-x+1)^3(x+2)^2(x-3) \)[/tex]
- Degree: 6
- Leading Coefficient: -1
2. [tex]\( f(x)=(-2 x+1)^2(x-3)^2(x+1) \)[/tex]
- Degree: 5
- Leading Coefficient: 4
3. [tex]\( f(x)=(x+6)(2 x-3)(x-1)^2 \)[/tex]
- Degree: 4
- Leading Coefficient: 2
4. [tex]\( f(x)=(x-2)^2(-2 x-1)^2(-x+1) \)[/tex]
- Degree: 5
- Leading Coefficient: -4
Now, let's match these functions to the given descriptions.
1. Degree: 4, leading coefficient: positive
The function [tex]\( f(x)=(x+6)(2 x-3)(x-1)^2 \)[/tex] fits this description.
- Degree: 4
- Leading Coefficient: 2 (positive)
2. Degree: 5, leading coefficient: negative
The function [tex]\( f(x)=(x-2)^2(-2 x-1)^2(-x+1) \)[/tex] fits this description.
- Degree: 5
- Leading Coefficient: -4 (negative)
3. Degree: 6, leading coefficient: negative
The function [tex]\( f(x)=(-x+1)^3(x+2)^2(x-3) \)[/tex] fits this description.
- Degree: 6
- Leading Coefficient: -1 (negative)
4. Degree: 5, leading coefficient: positive
The function [tex]\( f(x)=(-2 x+1)^2(x-3)^2(x+1) \)[/tex] fits this description.
- Degree: 5
- Leading Coefficient: 4 (positive)
Thus, we have the following matches:
1. [tex]\( f(x)=(x+6)(2 x-3)(x-1)^2 \)[/tex]: Degree: 4, leading coefficient: positive
2. [tex]\( f(x)=(x-2)^2(-2 x-1)^2(-x+1) \)[/tex]: Degree: 5, leading coefficient: negative
3. [tex]\( f(x)=(-x+1)^3(x+2)^2(x-3) \)[/tex]: Degree: 6, leading coefficient: negative
4. [tex]\( f(x)=(-2 x+1)^2(x-3)^2(x+1) \)[/tex]: Degree: 5, leading coefficient: positive
1. [tex]\( f(x)=(-x+1)^3(x+2)^2(x-3) \)[/tex]
- Degree: 6
- Leading Coefficient: -1
2. [tex]\( f(x)=(-2 x+1)^2(x-3)^2(x+1) \)[/tex]
- Degree: 5
- Leading Coefficient: 4
3. [tex]\( f(x)=(x+6)(2 x-3)(x-1)^2 \)[/tex]
- Degree: 4
- Leading Coefficient: 2
4. [tex]\( f(x)=(x-2)^2(-2 x-1)^2(-x+1) \)[/tex]
- Degree: 5
- Leading Coefficient: -4
Now, let's match these functions to the given descriptions.
1. Degree: 4, leading coefficient: positive
The function [tex]\( f(x)=(x+6)(2 x-3)(x-1)^2 \)[/tex] fits this description.
- Degree: 4
- Leading Coefficient: 2 (positive)
2. Degree: 5, leading coefficient: negative
The function [tex]\( f(x)=(x-2)^2(-2 x-1)^2(-x+1) \)[/tex] fits this description.
- Degree: 5
- Leading Coefficient: -4 (negative)
3. Degree: 6, leading coefficient: negative
The function [tex]\( f(x)=(-x+1)^3(x+2)^2(x-3) \)[/tex] fits this description.
- Degree: 6
- Leading Coefficient: -1 (negative)
4. Degree: 5, leading coefficient: positive
The function [tex]\( f(x)=(-2 x+1)^2(x-3)^2(x+1) \)[/tex] fits this description.
- Degree: 5
- Leading Coefficient: 4 (positive)
Thus, we have the following matches:
1. [tex]\( f(x)=(x+6)(2 x-3)(x-1)^2 \)[/tex]: Degree: 4, leading coefficient: positive
2. [tex]\( f(x)=(x-2)^2(-2 x-1)^2(-x+1) \)[/tex]: Degree: 5, leading coefficient: negative
3. [tex]\( f(x)=(-x+1)^3(x+2)^2(x-3) \)[/tex]: Degree: 6, leading coefficient: negative
4. [tex]\( f(x)=(-2 x+1)^2(x-3)^2(x+1) \)[/tex]: Degree: 5, leading coefficient: positive
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