How are the remainder and factor theorems useful?
You have only learned tools to factor quadratics; for higher degree polynomials, you can use long or synthetic division.
However, long/synthetic division is slow. If you guess the wrong divisor/factor, you will be wasting even more time.
Using the remainder theorem, we can quickly get the remainder with
This should lead you to try
Once you have a factor, you can proceed with long/synthetic division to get your quotient. Then you will need to repeat and factor the quotient. Again, if it is a quadratic, switch to your quadratic factoring methods.