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f(x)=3x^3+x^2-20 x+12 ,\ g(x)=3x-2...

`f(x)=3x^3+x^2-20 x+12 ,\ g(x)=3x-2`

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1409706 By using factor theorem
`(3x−2)=0`
`=>3x=2`
`=>x=2/3`
Now, Let `f(x)=3x^3+x^2−20x+12`
`f(2/3)=3(2/3)^3+(2/3)^2−20(2/3)+12`
`f(2/3)=3(8/27)+(4/9)−(40/3)+12`
`f(2/3)=(8/9)+(4/9)−(40/3)+12`
`f(2/3)=(12/9)−(40/3)+12`
`f(2/3)=(4/3)−(40/3)+12`
`f(2/3)=12−(36/3)`
`f(2/3)=12−12`
`f(2/3)=0`
`therefore (3x−2)` is a factor of `3x^3+x^2−20x+12`.
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