We started by looking at some problems with division of polynomials. Chose to use synthetic division, long division would be an option also.
To fully factor, for example, a fourth degree polynomial, if it comes out without a remainder then the combination of all factors is the fully factored form. Like you could factor 12 as 2*3*2.
Another problem seemed to call for the vertex form of a quadratic equation y = a(x-h)^2 + k where (h, k) is the vertex. Then you could convert that to standard form.
Talked a bit more about imaginary numbers.