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In this image, the problem asks you to find a factor of a polynomial \( X \), given that \( z = 5 \) is a root.

If \( z = 5 \) is a root of the polynomial, this means that \( X(5) = 0 \). By the factor theorem, if \( r \) is a root of a polynomial, then \( x - r \) is a factor of that polynomial.

In this case, since \( z = 5 \) is a root, a factor of the polynomial \( X \) is:

\[
x - 5
\]

Would you like more details or have further questions?

Here are 5 related questions to consider:
1. How do we derive factors from multiple roots of a polynomial?
2. What if the polynomial has complex roots, how do we express its factors?
3. Can you explain how to reconstruct a polynomial given all of its roots?
4. What is the difference between a factor and a divisor in polynomial theory?
5. How does the factor theorem relate to the division algorithm for polynomials?

**Tip:** If a root of a polynomial is repeated (for example, \( z = 5 \) appears twice), then \( (x - 5)^2 \) would be a factor of the polynomial.

Suppose z = 5 is a root of a polynomial X. A factor of X is ______.

Learn how to find the factor of a polynomial when z = 5 is given as a root. This problem explains the Factor Theorem and its application in determining polynomial factors, suitable for students in Grades 8-10.

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