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Math
A |
Factoring
Trinomials
(a = 1) |
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for this lesson
a will
always be 1.
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Whether
we use the FOIL method, or line up the factors vertically to multiply,
we all know that: 
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The
answer 
is called a trinomial.
To factor a trinomial of this form, we need to reverse the multiplication
process we used above. The process of factoring trinomials requires
that we develop our investigative skills.
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ATTENTION
Super Sleuths:
Look at all of the possible answers.
Check out your final answer to see that it really
works! |
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Let's see what
is involved with factoring
| 1. |
To get the
leading term of x², each first term must be x. So we start
with:
(x
) (x )
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| 2. |
The product of the
last terms must be -6. Possible answers 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 |
This tells us that our possible answers to
this problem will be:
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(x + 6)(x - 1)
(x - 6)(x + 1) (x +
3)(x - 2)
(x - 3)(x + 2) |
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| 3.
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You need to test each of these pairs to see which will yield
the correct middle term.
(x + 6)(x - 1) gives
middle term 5x.
(x - 6)(x + 1) gives
middle term -5x.
(x + 3)(x - 2) gives
middle term +x. YEA!!!!!
(x - 3)(x + 2) gives
middle term -x.
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| 4. |
Answer:
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You
may not need to list ALL of the possible answers when factoring
trinomials of this type. Simply ask yourself, "what
numbers will multiply to -6 and will add to +1?" |
Generally speaking, when the leading
coefficient is 1,
ask yourself
"what numbers multiply to the last term
and add to the middle term?"
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