Question

Is the binomial x-8 a factor of the function f(x)=x3^-9x^+12x-17 Explain

Answer 1

`(x-8)` is not a factor of the function
`f(x) = x^(3)-9\cdot x^(2)+12\cdot x - 17`.

Explanation:

If
`(x-8)` is a factor of the function
`f(x) = x^(3)-9\cdot x^(2)+12\cdot x - 17` if and only if
`f(8) = 0`. We must evaluate the polynomial at given value of
`x` to confirm or discard the statement:

`f(8) = 8^(3)-9\cdot (8)^(2)+12\cdot (8) -17`

`f(8) = 15`

Which means that
`(x-8)` is not a factor of the function
`f(x) = x^(3)-9\cdot x^(2)+12\cdot x - 17`.