Factoring: a General Strategy
We now combine all of our factoring techniques and consider a general strategy for factoring polynomials. Here we will encounter polynomials of all the types we have considered, in random order, so you will have the opportunity to determine which method to use.
FACTORING STRATEGY
To factor a polynomial:
a) Always look first for a common factor. If there is one, factor out the largest common factor.
b) Then look at the number of terms.
Two terms: Determine whether you have a difference of squares,
A2 – B2. Do not try to factor a sum of squares: A2 + B2 .
Three terms: Determine whether the trinomial is a square. If it is, you know how to factor. If not, try trial and error, using FOIL or the ac-method.
Four terms: Try factoring by grouping.
c) Always factor completely. If a factor with more than one term can still be factored, you should factor it. When no factor can be factored further, you have finished.
d) Check by multiplying.