Question

Is (x-4) a factor of f(x)=x^3-2x^2+5x+1 explain your reasoning

Answer 1

No.

Explanation:

It's simpler than you might expect.

If
`(x - 4)` is a factor, then it means that it the function
`f(x) = x^3 - 2x^2 + 5x + 1` can have
`(x - 4)` factorised out.

This means that we can say
`(x - 4) = 0`

Therefore
`x = 4`

If we put
`x = 4` into the equation:

`f(4) = (4)^3 - 2(4)^2 + 5(4) + 1\\= 64 - 32 + 20 + 1\\= 53`

We didn't get 0, therefore it isn't a factor!