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for this lesson
a will
NOT be 1.
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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.
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When
the leading coefficient is a number other than one, the
number of possible answers increases ..... making our
investigative efforts harder. |
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Let's see what
is involved with factoring
 .
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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.
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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.
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| 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:
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(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) |
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| 4.
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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.
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| 5. |
Answer:
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. |
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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!!! |
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|
 |
See how to use
your
TI-83+ /84+ graphing calculator with
factoring.
Click calculator. |
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1)