Section 3.3
Homework Questions?
Section 3.3
Factoring Trinomials: AC-Method
Concepts
1. Factoring Trinomials by the AC-Method
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Section 3.3
Factoring Trinomials: AC-Method
1. Factoring Trinomials by the AC-Method
by the acTo factor a quadratic trinomial,
method, we rewrite the middle term, bx, as a sum or
difference of terms. The goal is to produce a four-term
polynomial that can be factored by grouping.
Remember the trinomial must be in descending order (in
the form
) before beginning the factoring
process.
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PROCEDURE AC-Method: Factoring ax2 + bx + c
(a 0)
Step 1 Factor out the GCF from all terms.
Step 2 Multiply the coefficients of the first and last
terms.
Step 3 Find two integers whose product is and whose
sum is b. (If no pair of integers can be found,
then the trinomial cannot be factored further
and is a prime polynomial.)
Step 4 Rewrite the middle term, bx, as the sum of
two terms whose coefficients are the integers
found in step 3.
Step 5 Factor the polynomial by grouping.
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Example 1
Factoring a Trinomial by the AC
Method
Factor the trinomial by the ac-method:
3x2  11x  6
Example 2
Solution:
Factoring a Trinomial by the AC
Method
Factor the trinomial by the ac-method:
4 x 2  14 x  7
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Example 3
Solution:
Factoring a Trinomial by the AC
Method
Factor the trinomial by the ac-method:
2 x 2  x  10
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Example 4
Factoring a Trinomial by the AC
Method
Solution:
Factor the trinomial by the ac-method:
6 x 2  17 x  10
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Example 5
Factoring a Trinomial by the AC
Method
Solution:
Factor the trinomial by the ac-method:
2 x2  7 x  6
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TIP: One frequently asked question is whether the
order matters when we rewrite the middle term of the
trinomial as two terms (step 3). The answer is no. From
the previous example, the two middle terms in step 3
could have been reversed to obtain the same result:
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Example 6
Factoring Trinomials by the ACMethod
Factor the trinomial by the ac-method:
Example 7
Solution:
Factoring Trinomials by the ACMethod
Factor the trinomial by the ac-method:
4  24 x  11x 2
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Example 8
Factoring a Trinomial by the ACMethod
Factor the trinomial by the ac-method:
Example 9
Factor:
Factoring a Trinomial by the ACMethod
Example 10
Factoring a Trinomial by the ACMethod
Factor the trinomial by the ac-method:
Section 3.3
Factoring Trinomials: AC-Method
You Try
Factor the trinomial by the ac-method
a. 6 x2  5x  6
b. 3x2  20 x  12
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Section 3.3
Factoring Trinomials: AC-Method
You Try
Factor the trinomial by the ac-method
a. 3x3  23x2 14x
b. 40 y  24x2 y  76xy
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