If one of the roots of a polynomial is $x = 2$, we know that $(x - 2)$ is a factor of that polynomial. To construct a polynomial that has $x = 2$ as one of its roots, we need to determine the other factors, if any, and the degree of the polynomial.

For example:

1. If $x = 2$ is the only root (and the polynomial is linear), the equation would be: $f(x) = a(x - 2)$ where $a$ is a constant.

2. If $x = 2$ is one of the roots and there is another root, say $x = 3$, the polynomial would be: $f(x) = a(x - 2)(x - 3)$

3. For a quadratic with repeated root $x = 2$ (a double root), the polynomial would be: $f(x) = a(x - 2)^2$

In general, given the root $x = 2$, the polynomial can take different forms depending on its degree and the other roots (if any).

Would you like a detailed explanation of how to expand these examples?

Related questions:

1. How do I determine the degree of a polynomial if I know some of its roots?
2. How can I find the other roots