How You Can (And Should) Get More Practice!

Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for you.

Theoretically Easier Difficulty Problem

Start by finding all numbers that evenly divide the constant term.
The previous list is all the possible zeros by the rational root theorem - time to guess and check. This is why this is a tool of last resort.
Factor the following polynomial (hint: Using the Rational Root Theorem to get a zero, then divide out the factor to reduce the polynomial)

Theoretically Medium Difficulty Problem

Start by finding all numbers that evenly divide the constant term, and another list of all the terms that evenly divide the leading coefficient.
Make a list of every combination of a factor that divides the constant divided by a factor that divides the leading coefficient. This is the list of all possible zeros - time to guess and check!
Factor the following polynomial (hint: Using the Rational Root Theorem to get a zero, then divide out the factor to reduce the polynomial)

Theoretically Harder Difficulty Problem

Start by finding all numbers that evenly divide the constant term, and another list of all the terms that evenly divide the leading coefficient.
Make a list of every combination of a factor that divides the constant divided by a factor that divides the leading coefficient. This is the list of all possible zeros - time to guess and check!
Factor the following polynomial (hint: Using the Rational Root Theorem to get a zero, then divide out the factor to reduce the polynomial)