Before factoring using ax2+bx+c, two other types of factoring should be tested.
a) Explain how these two types may simplify your work.
You can generally do the box method or the X method, with the multiples and the coefficients multiplying each other and then summing to get the B term: However, there are other couple notable methods for factoring quadratics:
For example, if you notice there is no B term, you can try difference of squares if c is negative
Another example is factor by grouping. You can do this by splitting up the B term into two different terms, and then take out the GCF of each group, and then using distributive property (but reversed).
For example: 2x^2 + 5x + 2.
2x^2 + 4x + x + 2
2x(x + 2) + 1(x + 2)
(2x + 1)(x + 2)
I hope you don't mean factoring as vertex form or expanded form...