AR Day 5 Factoring Trinomials.notebook
AR Day 5: Factoring Trinomials
Objecves:
1. To completely factor trinomial expressions. Factoring a trinomial is the reverse process of mulplying.
x2 + 2x + 1
(x + 1)(x + 1)
(x + 1)2
The first thing to ALWAYS look for when beginning to factor is that the trinomial is in descending order AAAAAND look for the GCF!!!!!!!!
6x ‐ 2x3 ‐ 4x2 Descending order: ‐2x3 ‐ 4x2 + 6x
GCF: ‐2x
(because the lead term is negave)
‐2x(x2) + (‐2x)(2x) ‐ (‐2x)(3)
‐2x(x2 + 2x ‐ 3)
‐2x(x + 3)(x ‐ 1)
A trinomial that is not factorable is called Prime.
Example: x2 + 2x + 2
Mar 28­6:52 AM
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AR Day 5 Factoring Trinomials.notebook
Completely Factor:
7x + 2x2 ­ 4
General Form of a trinomial:
ax2 + bx + c
Step 1:
Is the trinomial in descending order?
*If yes, connue.
*If no, rewrite in descending order.
Is there a GCF?
*If yes, factor it out
*If no, connue.
Step 2:
Set up the "diamond" to find your factors.
Mar 28­7:04 AM
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AR Day 5 Factoring Trinomials.notebook
Factor:
3n2 ‐ 7n ‐ 6
x2 + 8x + 15
18x2 + 33x ‐ 30
2x2 + 26x ‐ 96
Mar 28­7:40 AM
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AR Day 5 Factoring Trinomials.notebook
Factoring Thought Process
Binomial
Trinomial
*Factor out GCF if one exists.
*Write in descending order first.
*Then factor out GCF if one exists.
"Adding"
NO
Prime
*if no GCF was
factored out
"Subtracting"
Both terms Perfect Square?
*Ex: x2 ­ 16
YES
ax2 + bx + c
*Set Up "Diamond" Problem
a*c
*Multiplies to get the top
b
Factor into:
(a ­b)(a+b)
*Adds to get the bottom
*Rewrite trinomial as four terms.
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g is
*Factor by Grouping
*Factor GCF of 1st two terms
*Then 2nd pair of terms
*Factor out the "grouping"
Example:
6x2 + x ­ 12
­72
­8
9
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6x2 + 9x ­ 8x ­ 12
3x(2x + 3) ­ 4(2x + 3)
(2x + 3)(3x ­ 4)
Apr 26­1:49 PM
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