We are given a function $f(x)$ and its values at $x = 0, 1, -1, 2$. We have $f(1) = 0$, $f(2) = 64$, $f(-1) = -24$, and $f(0) = -20$. We need to determine which value of $x$ is a factor of the function. A factor of the function is a value $x=a$ such that $f(a) = 0$.

1. Problem Description

We are given a function $f(x)$ and its values at $x = 0, 1, -1, 2$. We have $f(1) = 0$, $f(2) = 64$, $f(-1) = -24$, and $f(0) = -20$. We need to determine which value of $x$ is a factor of the function. A factor of the function is a value $x=a$ such that $f(a) = 0$.

2. Solution Steps

We are given the values of $f(x)$ at four different points.

A factor of the function $f(x)$ is a value $a$ such that $f(a) = 0$. This is equivalent to $x-a$ being a factor of the polynomial $f(x)$.

We are given the following values:

$f(1) = 0$

$f(2) = 64$

$f(-1) = -24$

$f(0) = -20$

Since $f(1) = 0$, $x = 1$ is a root of the function.

Therefore, $x - 1 = 0$, which means that when $x = 1$, we have a factor.

3. Final Answer

x=1