Factoring Trinomials (a 1) Set-Up, Guess, and Check Method Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

 for this lesson a will NOT be 1.

In the Algebra lesson on factoring trinomials where a = 1, we learned that factoring may require that we put our investigative skills to work.  Those skills will really be put to the test when our trinomial starts with an a-value other than one.  As with all factoring, there are several different methods that may be used.  Let's see what is involved in the "Set-up, Guess and Check" Method.

 When the leading coefficient is a number other than one, the number of possible answers increases ..... making our investigative efforts harder.

Let's see what is involved with factoring  .

1. First, check to see if all of the terms share a common factor which may be removed.  If each term can be factored before you begin, your work will be easier.  The terms in this problem do not have a common factor.

2.

Consider all of the possible factors of the leading coefficient, 2x².  In this problem we only have one choice, 2x and x, making our work easy.  So we can start with:
(2x       ) (x       )
If the leading coefficient has several factors, make a list of the possible combinations, so as to be sure to include all possibilities.

3. Consider all of the possible factors of the last term, -6.  The possible factors are:
 +6 and -1 -6 and +1 +3 and -2 -3 and +2 You need to consider all of the possible ways of obtaining  the number -6.

It appears that we have a multitude of "possible" answers:

 (2x + 6)(x - 1) (2x - 6)(x + 1) (2x + 3)(x - 2) (2x - 3)(x + 2) (x + 6)(2x - 1) (x - 6)(2x + 1) (x + 3)(2x - 2) (x - 3)(2x + 2)

4.

We need to find the one "true" answer that will produce the desired middle term of -x.  Test each of the possible answers to see which will yield the correct middle term.
(2x + 6)(x - 1)
gives middle term 4x.
(2x - 6)(x + 1)
gives middle term -4x.
(2x + 3)(x - 2)
gives middle term -x.  YEA!!!!!
(2x - 3)(x + 2)
gives middle term +x.
(x + 6)(2x - 1)  gives middle term 11x.
(x - 6)(2x + 1)
gives middle term -11x.
(x + 3)(2x - 2)
gives middle term 4x.
(x - 3)(2x + 2)
gives middle term -4x.

Notice:  While we initially had several options for answers, we really had only one true answer.  The more options that a problem creates, the more detective work needed to find the true answer.

 Unfortunately, there is no "short cut" with this method - (other than doing some of the thinking mentally). But don't let it drive you crazy ... just slowly and systematically examine your possible answers until you find the one that yields the correct middle term.  It can be done!!!  You can do it!!!

 See how to use your TI-83+ /84+ graphing calculator  with factoring. Click calculator.

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