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I. Model Problems.
II. Practice
III. Challenge Problems
VI. Answer Key
Web Resources
How To Factor Trinomials (step by step)
www.mathwarehouse.com/algebra/factor/how-to-factor-trinomials-step-by-step.php
Methods of Factoring
http://www.mathwarehouse.com/algebra/factor/methods-of-factoring.php
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Factoring Trinomials (including difference of squares)
I. Model Problems
In the following examples you will factor a quadratic trinomial.
Example 1: Factor
Factor the trinomial as a product of two binomials by undoing FOIL.
For
we want to find p and q such that
and
List the factors of
.
Find the sum of the factors. We are looking for 3.
Substitute factors of
or…
Check with FOIL.
.
;
;
;
with a sum of 3.
Answer:
Example 2: Factor
In this case the outside and inside term will be multiplied before we find the sum
The factors of 3 are 3 and 1. The first terms of the
binomials are 3x and 1x.
List the factors of .
;
If a factor is in the ‘outside’ slot it is multiplied by 3
before we find the sum. If a factor is in the ‘inside’
Sum
slot it is multiplied by 1.
17
43
13
23
Substitute factors into the correct slot.
Check with FOIL.
Answer:
In the following examples you will factor a difference of squares.
Example 3: Factor
Rewrite as trinomial.
We are looking for the factors of
that have a sum of 0.
Answer:
For difference of squares:
;
;
.
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II. Practice Problems
Factor.
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9. x 2  7 x  12
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III. Challenge Problems
Factor completely.
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25. Find the mistake in the following.
x2 + 2x − 48
(x + 6)(x - 8)
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IV. Answer Key
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17. not factorable
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25. Right magnitude of factors, but the signs are switched.
Should be (x − 6)(x + 8)
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