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f(x)=x^3-6x^2-19 x+84 ,\ g(x)=x-7...

`f(x)=x^3-6x^2-19 x+84 ,\ g(x)=x-7`

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`f(x)=x^3-6x^2-19x+84`
`g(x)=x-7`
By the factor theorem, `g(x)` is the factor of polynomial `f(x)` if `f(7)=0`
`(x-7)`
`=>x=7`
`f(7)=0`
Now,
`f(7)=(7)^3-6(7)^2-19(7)+84`<>`=343-294-133+84`
`=427-427`
`=0`
`therefore (x-7)` is a factor of polynomial `f(x)`.
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