describe a strategy for factoring a polynomial. Give an example showing all of your steps. Also show check?

Answer 1

The factors are where y=0. If it is quadratic, I use the formula, which I'm sure you know. For polynomials of greater power I use derivatives to help me find if there are maxima and/or minima that tell me where a function "turns" in a two-dimensional space. Then I can find the cross-over points or determine if the roots are imaginary (no cross-over).

For checking, I simply multiply the expressions together to see if the original polynomial come out.