Jedi Factor Trial Slides Force of Factors
Jedi Mastery Training
Unlock the secrets of GCF and Difference of Squares
The Mission
Objective 1: GCF Extraction
Identify and remove the Greatest Common Factor from galactic codes (polynomials).
Objective 2: Square Sabotage
Recognize the Difference of Squares pattern to dismantle Sith security systems.
"Do or do not. There is no try...
The Force of GCF
Definition
The largest term that divides evenly into every term of the polynomial.
The Protocol:
Find GCF of coefficients
Find GCF of variables (lowest power)
Divide and rewrite: GCF(...)
Trial 1: Factor \(6x^3 - 12x^2 + 18x\)
1
GCF of 6, 12, 18 is 6
2
GCF of \(x^3, x^2, x\) is \(x\)
Solution:
\(6x(x^2 - 2x + 3)\)
Difference of Squares
\[a^2 - b^2 = (a - b)(a + b)\]
Security Checklist:
Must be a subtraction (Difference)
Both terms must be perfect squares
Always check for a GCF first!
Trial 2: \(25x^2 - 49\)
1. Square root of \(25x^2\) is \(5x\)
2. Square root of \(49\) is \(7\)
Solution: \((5x - 7)(5x + 7)\)
Combined Tactics
Advanced Defense
Master Trial: \(2x^2 - 18\)
Step 1
Check for GCF. Both terms divide by 2.
\(2(x^2 - 9)\)
Step 2
Check inside parenthesis. \(x^2 - 9\) is a Difference of Squares!
\(2(x - 3)(x + 3)\)
Holocron Hunt Rules
Draw a Kyber Crystal Card.
Identify the GCF of the polynomial first.
Factor completely on your Star Map.
If correct, move your ship forward one parsec (square).
Reach the final Holocron to secure galactic peace!
MAY THE FACTORS BE WITH YOU
Kyber Crystal Cards Kyber Crystal Cards
Holocron Hunt: Polynomial Factoring Tasks
Cut along dashed lines. 24 unique trial codes.
Level 1: GCF ID: KC-01
\(5x + 10\)
Level 1: GCF ID: KC-02
\(3x^2 - 12x\)
Level 1: GCF ID: KC-03
\(8x^3 + 12x^2\)
Level 1: GCF ID: KC-04
\(7x - 21y\)
Level 2: Squares ID: KC-05
\(x^2 - 16\)
Level 2: Squares ID: KC-06
\(y^2 - 100\)
Level 2: Squares ID: KC-07
\(4x^2 - 9\)
Level 2: Squares ID: KC-08
\(25a^2 - 1\)
Level 3: Combo ID: KC-09
\(2x^2 - 8\)
Level 3: Combo ID: KC-10
\(3y^2 - 75\)
Level 3: Combo ID: KC-11
\(5x^2 - 20\)
Level 3: Combo ID: KC-12
\(10x^2 - 90\)
Star Map Board Star Map
Galactic Sector: Factoria
Squadron Name
Start
1
2
3
4 Warp
5
11
10
9
8
7
6
12
13
Asteroids:
15
16
17
23
22
21
20
19
18
24
25
26
27
28
Holocron Victory!
Movement
Each correct factorized polynomial moves your ship forward 1 parsec (square). Record every solution on your Log.
Sith Guards
If you get a factor wrong, you must stay in place and complete a training trial (review) before moving again.
The Prize
The first squadron to secure the Holocron receives the title of Factor Masters and 500 Galactic Credits (Bonus points).
Factor Flight Log Worksheet Factor Flight Log
Sector: Factoria | Mission: Holocron Hunt
Squadron Pilot
Stardate
Navigation Protocol
Record the ID of each Kyber Crystal Trial. Show all mathematical work clearly in the diagnostic area. Once the polynomial is fully factorized, call for a Commander (Teacher) or check with your Squadron to confirm movement on the Star Map.
Trial ID: _______
Diagnostic Area (Show Work):
Final Factorized Code:
Trial ID: _______
Diagnostic Area (Show Work):
Final Factorized Code:
Trial ID: _______
Diagnostic Area (Show Work):
Final Factorized Code:
Trial ID: _______
Diagnostic Area (Show Work):
Final Factorized Code:
Trial ID: _______
Diagnostic Area (Show Work):
Final Factorized Code:
Trial ID: _______
Diagnostic Area (Show Work):
Final Factorized Code:
Trial ID: _______
Diagnostic Area (Show Work):
Final Factorized Code:
Trial ID: _______
Diagnostic Area (Show Work):
Final Factorized Code:
Holocron Master Key Answer Key Holocron Master Key
Teacher Reference | Kyber Crystal Solutions
Level 1: GCF Extraction
KC-01
\(5x + 10\)
\(5(x + 2)\)
KC-02
\(3x^2 - 12x\)
\(3x(x - 4)\)
KC-03
\(8x^3 + 12x^2\)
\(4x^2(2x + 3)\)
KC-04
\(7x - 21y\)
\(7(x - 3y)\)
Level 2: Square Sabotage
KC-05
\(x^2 - 16\)
\((x - 4)(x + 4)\)
KC-06
\(y^2 - 100\)
\((y - 10)(y + 10)\)
KC-07
\(4x^2 - 9\)
\((2x - 3)(2x + 3)\)
KC-08
\(25a^2 - 1\)
\((5a - 1)(5a + 1)\)
Level 3: Master Tactics (Combo)
KC-09
\(2x^2 - 8\)
\(2(x - 2)(x + 2)\)
KC-10
\(3y^2 - 75\)
\(3(y - 5)(y + 5)\)
KC-11
\(5x^2 - 20\)
\(5(x - 2)(x + 2)\)
KC-12
\(10x^2 - 90\)
\(10(x - 3)(x + 3)\)
Facilitation Tips
Students should play in pairs or small "Squadrons."
Encourage students to verify each other's work using the log before moving on the map.
For "Asteroid" spaces, students must wait one turn before picking a new card.
The "Warp" space (Space 4) allows a student to move ahead to Space 10 if they correctly factor a Level 3 card immediately.
