Explanation:

Intersecting x-axis at exactly two points
- When the graph of a polynomial intersects the x-axis at exactly two points, it means that the polynomial has two real roots.
- This implies that the polynomial can be factored into linear factors, as each real root corresponds to a factor of the form (x - a), where 'a' is the root.
- Therefore, if the graph intersects the x-axis at exactly two points, the polynomial can be expressed as a product of two linear factors.

Characteristics of the graph
- The graph of a polynomial intersects the x-axis at the real roots of the polynomial.
- If a polynomial has two real roots, the graph will intersect the x-axis at these two points.
- The multiplicity of the roots determines how the graph behaves at these points. If both roots have multiplicity 1, the graph will cross the x-axis at these points. If one root has multiplicity 2, the graph will touch the x-axis and turn around at that point.

Conclusion
- In conclusion, if the graph of a polynomial intersects the x-axis at exactly two points, it indicates that the polynomial has two real roots, which can be expressed as linear factors.
- Understanding the characteristics of the graph of a polynomial can help in determining the behavior of the polynomial at these points and interpreting the relationship between the graph and the roots of the polynomial.