To determine which graph could represent a degree-4 polynomial with $(x-1)$ as one of its factors, consider the following key features:

Characteristics of a degree-4 polynomial:

1. A degree-4 polynomial has up to 4 roots (real or complex), and the graph may cross or touch the x-axis at these roots.
2. The polynomial's end behavior depends on the leading coefficient:
   • Positive leading coefficient: The graph rises on both ends.
   • Negative leading coefficient: The graph falls on both ends.
3. If $(x-1)$ is a factor, then $x=1$ is a root, meaning the graph must intersect or touch the x-axis at $x=1$.

Possibilities for the root $x=1$:

1. If the factor $(x-1)$ appears once (has odd multiplicity), the graph crosses the x-axis at $x=1$.
2. If the factor $(x-1)$ appears twice (has even multiplicity), the graph touches but does not cross the x-axis at $x=1$.

Steps to Identify the Correct Graph:

1. Locate $x=1$ on the graph and check whether the curve either crosses or touches the x-axis there.
2. Ensure the graph shows at most four x-intercepts or turning points.
3. Verify that the overall shape (end behavior) aligns with the characteristics of a degree-4 polynomial.

Could you provide the graphs or additional descriptions so we can analyze them further? If not, we can discuss general examples!