In polynomial long division, what is done after multiplying the term found in step 1 by the divisor?

In polynomial long division, after you multiply the term obtained in the first step by the divisor, the next action is to subtract that product from the section of the dividend you are currently working with. This step is crucial because it updates the polynomial you are dividing by removing the part that has been accounted for, allowing you to focus on the remaining terms. By subtracting, you reveal the new remainder that will be used in the next steps of the division process.

This subtraction is a fundamental part of the long division algorithm, similar to what is done in numerical long division. It ensures that the process moves forward correctly, gradually simplifying the polynomial until the entire dividend has been addressed. This step sets the stage for the next iteration of division, where you would again look for how many times the leading term of the divisor can fit into the new remainder.