Question

Which function is (x-1) a real root?

Answer 1

D

Explanation:

According to the Factor Theorem:

In order for a factor in the form of
`(x-a)` to be a root for a function
`f(x)`,
`f(a)` must be 0.

Our factor is
`(x-1)`.

Therefore,
`a=1`.

So, we will evaluate
`f(1)` for all the choices.

Doing so, we can see that, starting from the top, we have:

`\begin{aligned}f_1(1)&=-12\\ f_2(1) &=8 \\ f_3(1)&=24 \\ f_4(1)&=0 \end{aligned}`

The choice that yields 0 as an answer is D.

So, the function for which
`(x-1)` is a real root is choice D.