Question

Why is it useful to factor polynomial expressions for a given scenario?

Answer 1

To determine the roots or the zeros of the polynomial. These are the  x-intercepts.

Answer 2

Whether it is useful or not depends on the scenario.

If the scenario involves finding zeros, or simplifying rational functions, then finding factors that can be cancelled or set to zero will aid in performing the task. In a scenario where a polynomial represents a differential equation, finding the factors can help determine the behavior of the solution to the equation.

If the scenario involves finding extremes or end-point behavior, factoring may be a waste of time.