Blueprint Anchor Chart Factor Fortress
The Blueprint for Factoring Quadratics
Project Status Approved
1
Identify the GCF
Look for the biggest number that divides into every term. Pull it out to the front!
12x² + 30x - 18 6(2x² + 5x - 3)
2
Build the "X"
Identify a = 2, b = 5, c = -3
Multiply a × c for the TOP.
Place b on the BOTTOM.
a × c = -6
b = 5
6
-1
Find numbers that multiply to TOP and add to BOTTOM!
3
Split & Group
Replace the middle term with your two magic numbers, then factor by grouping.
Split: 2x² + 6x - 1x - 3
Group: (2x² + 6x) + (-1x - 3)
Factor: 2x(x + 3) - 1(x + 3)
Final Blueprint
6(2x - 1)(x + 3)
Don't forget to put your GCF back in front!
Construction Crew Slides Factor Fortress
Building Quadratics Step-by-Step
The Challenge
New Project
How do we factor this completely?
12x² + 30x - 18
GCF First
X-Method
Grouping
1
Clear the Site (GCF)
What is the largest number that goes into 12, 30, and 18?
The GCF is 6!
12 / 6 = 2
30 / 6 = 5
18 / 6 = 3
6(2x² + 5x - 3)
"Save the 6 for the end!"
2
Design the Blueprint
2x² + 5x - 3
a × c 2 × -3 = -6
b 5
-6
5
3
Find the Magic Numbers
-6
5
6
-1
The Rules:
Multiply to -6
Add to 5
6 × -1 = -6
6 + (-1) = 5
4
The Great Split
We replace 5x with our magic numbers: 6x and -1x.
2x² + 5x - 3
2x² + 6x - 1x - 3
5
Final Assembly (Grouping)
Group It (2x² + 6x) + (-1x - 3)
Pull GCFs
2x(x + 3) - 1(x + 3)
Wait! The parentheses match!
Factor (2x - 1)(x + 3)
Warning!
Don't forget your original GCF!
Our final factored answer is:
6(2x - 1)(x + 3)
Site Secured
Built to Last
Construction Site Worksheet Construction Site Practice
Building Factors from the Ground Up
Worker:
Shift Date:
Follow the blueprint steps: GCF → X-Method → Grouping. Show every step of the build!
1
6x² + 21x - 12
Step 1: Identify & Pull GCF
Step 2: Build the X (a × c and b)
Step 3: Split & Grouping Work Area
Final Blueprint (Factored Form)
2
8x² + 28x + 12
Step 1: Identify & Pull GCF
Step 2: Build the X
Step 3: Split & Grouping Work Area
Final Blueprint (Factored Form)
Foreman Answer Key Foreman's Answer Key
Verification Master Blueprint
1
6x² + 21x - 12
Step 1: Identify & Pull GCF
3(2x² + 7x - 4)
Step 2: Build the X (a × c and b)
-8
7
8
-1
Step 3: Split & Grouping Work Area
3(2x² + 8x - 1x - 4)
3[(2x² + 8x) + (-1x - 4)]
3[2x(x + 4) - 1(x + 4)]
Final Blueprint (Factored Form)
3(2x - 1)(x + 4)
2
8x² + 28x + 12
Step 1: Identify & Pull GCF
4(2x² + 7x + 3)
Step 2: Build the X
6
7
6
1
Step 3: Split & Grouping Work Area
4(2x² + 6x + 1x + 3)
4[(2x² + 6x) + (1x + 3)]
4[2x(x + 3) + 1(x + 3)]
Final Blueprint (Factored Form)
4(2x + 1)(x + 3)