check whether g(x) is a factor of f(x) or not f(x)=`x^5+3x^4−x^3−3x^2+5x+15`, g(x)=`x+3`

Explanation

`f(x)=x^5+3x^4-x^3-3x^2+5x+15`
`g(x)=x+3`
By the factor theorem, `g(x)` is the factor of polynomial `f(x)`.
Then,
`x+3=0`
`=>x=-3`
Putting the `x=-3` in `f(x)`
`f(-3)=(-3)^5+3(-3)^4-(-3)^3-3(-3)^2+5(-3)+15`
`f(-3)=0`
`therefore g(x)` is the factor of polynomial `f(x)`.