Question

How do you use the factor theorem to determine whether x-5 is a factor of `f(x) = 2x^3 +5x^2 -14x -72`?

Answer 1

`x-5` is not a factor of `f(x)`

Explanation:

To see if `(x-5)` is a factor of `f(x)` we have to check if `f(5)=0`

`f(5)=2*5^3+5*5^2-14*5-72`

`f(5)=250+125-70-72`

`f(5)=375-142`

`f(5)=233`

`f(5)!=0` so `(x-5)` is not a factor of `f(x)`