Which of the following is a factor of x4 + 5x3 - 4x2 - 8x + 6?
2x+3
x-1
2x-3
x+1
2 answers:
Answer:
The correct option is 2.
Step-by-step explanation:
The given function is
![f(x)=x^4+5x^3-4x^2-8x+6](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E4%2B5x%5E3-4x%5E2-8x%2B6)
If (x-c) is a factor of a function, then f(c)=0.
In option 1:
![(2x+3)=0](https://tex.z-dn.net/?f=%282x%2B3%29%3D0)
![x=-\frac{3}{2}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B3%7D%7B2%7D)
![f(-\frac{3}{2})=(-\frac{3}{2})^4+5(-\frac{3}{2})^3-4(-\frac{3}{2})^2-8(-\frac{3}{2})+6=\frac{-45}{16}\neq 0](https://tex.z-dn.net/?f=f%28-%5Cfrac%7B3%7D%7B2%7D%29%3D%28-%5Cfrac%7B3%7D%7B2%7D%29%5E4%2B5%28-%5Cfrac%7B3%7D%7B2%7D%29%5E3-4%28-%5Cfrac%7B3%7D%7B2%7D%29%5E2-8%28-%5Cfrac%7B3%7D%7B2%7D%29%2B6%3D%5Cfrac%7B-45%7D%7B16%7D%5Cneq%200)
Therefore option 1 is incorrect.
In option 2:
![x-1=0\Rightarrow x=1](https://tex.z-dn.net/?f=x-1%3D0%5CRightarrow%20x%3D1)
![f(1)=(1)^4+5(1)^3-4(1)^2-8(1)+6=0](https://tex.z-dn.net/?f=f%281%29%3D%281%29%5E4%2B5%281%29%5E3-4%281%29%5E2-8%281%29%2B6%3D0)
Therefore option 2 is correct and (x-1) is a factor of f(x).
In option 3:
![(2x-3)=0](https://tex.z-dn.net/?f=%282x-3%29%3D0)
![x=\frac{3}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B2%7D)
![f(\frac{3}{2})=(\frac{3}{2})^4+5(\frac{3}{2})^3-4(\frac{3}{2})^2-8(\frac{3}{2})+6=\frac{111}{16}\neq 0](https://tex.z-dn.net/?f=f%28%5Cfrac%7B3%7D%7B2%7D%29%3D%28%5Cfrac%7B3%7D%7B2%7D%29%5E4%2B5%28%5Cfrac%7B3%7D%7B2%7D%29%5E3-4%28%5Cfrac%7B3%7D%7B2%7D%29%5E2-8%28%5Cfrac%7B3%7D%7B2%7D%29%2B6%3D%5Cfrac%7B111%7D%7B16%7D%5Cneq%200)
Therefore option 3 is incorrect.
In option 4:
![x+1=0\Rightarrow x=-1](https://tex.z-dn.net/?f=x%2B1%3D0%5CRightarrow%20x%3D-1)
![f(-)=(-1)^4+5(-1)^3-4(-1)^2-8(-1)+6=6\neq 0](https://tex.z-dn.net/?f=f%28-%29%3D%28-1%29%5E4%2B5%28-1%29%5E3-4%28-1%29%5E2-8%28-1%29%2B6%3D6%5Cneq%200)
Therefore option 4 is incorrect.
Answer:
x + 1
Step-by-step explanation:
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