Why does the GCF become one of the solutions to a polynomial?

GCF is one of the solutions because it divides evenly through all factors or a polynomial expression such that when multiplied by other factors results in the given polynomial expression

Step-by-step explanation:

GCF, the greatest common factor of a group of given polynomials is the largest polynomial that divides evenly into the polynomials.

Example 25b³+10b²

The GCF is 5b² which is common to both terms and can divide through both terms