Answer:
D
Step-by-step explanation:
According to the Factor Theorem:
In order for a factor in the form of [tex](x-a)[/tex] to be a root for a function [tex]f(x)[/tex], [tex]f(a)[/tex] must be 0.
Our factor is [tex](x-1)[/tex].
Therefore, [tex]a=1[/tex].
So, we will evaluate [tex]f(1)[/tex] for all the choices.
Doing so, we can see that, starting from the top, we have:
[tex]\begin{aligned}f_1(1)&=-12\\ f_2(1) &=8 \\ f_3(1)&=24 \\ f_4(1)&=0 \end{aligned}[/tex]
The choice that yields 0 as an answer is D.
So, the function for which [tex](x-1)[/tex] is a real root is choice D.
