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

Discover how to solve polynomial equations when one of the roots is x=2. This step-by-step guide covers key algebraic concepts such as factorization and the use of the root theorem. Suitable for students in Grades 9-12.

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