I have 2 questions for an assignment.

1 Factorise the expression below using the factor theorem. Use polynomial division to evaluate a quotient and remainder in your method.

and 2

Factorise the expression below using the remainder theorem.

Both of these are easy to factorise but when we covered the factor and remainder theorems in class they kind of merged together and I cant work out which is which!

I know that evaluating f(a) gives 0 when (x - a) is a valid factor which you then divide by to get the quotient which is what I have done for the first one, but for the second one I am assuming I have to do the full polynomial division for each trail factor just keeping the ones that factor out to a 0 remainder?

any clarification on the distinction between these theorems?

Thanks