Wetzel 

Math 101

6.3 – Factoring Trinomials where a ≠ 1

Factor by Trial and Error:

            Steps:

            1.)  Factor Out any Common Factors making sure the leading term is positive

            2.)  List the factors of the first and last terms. (write as pairs)

            3.)  A pair of factors from the first term will become the first terms in the binomials and a pair of factors from the second term will become the second terms in the binomials.  Use trial and error to determine which pair to choose.

            4.)  Determine the signs in the binomials. 

            5.)  Check your factoring by multiplying back through.  If you do not come up with your original trinomial, check for any mistakes or different factors.  If there are no other options, the trinomial is PRIME.

Ex.:  Factor

1.)          2.)         3.) 

Factor by Grouping:

            Steps:

            1.)  Factor Out any Common Factors making sure the leading term is positive

            2.)  Multiply a · c

            3.)  Find two numbers whose product is a · c and whose sum is b

            4.)  Rewrite the term bx as two terms using the two integers found in Step 3.

            5.)  Factor the resulting polynomial by grouping.

Ex.:  Factor

4.)         5.)                6.)