Factor Finding Slides
Factor Finding
Unlocking the Building Blocks of Algebra
01 // THE CONCEPT
What is Factoring?
Factoring is the reverse of multiplying (distributing).
Distribution:
2(x + 3) → 2x + 6
Factoring:
2x + 6 → 2(x + 3)
"We are looking for the common pieces that were multiplied together to create the expression."
02 // THE GCF
Greatest Common Factor
The **GCF** is the largest term that divides evenly into every term in the expression.
Example: \(12x^2 + 18x\)
- Numbers: GCF of 12 and 18 is **6**.
- Variables: GCF of \(x^2\) and \(x\) is **\(x\)**.
- Total GCF: \(6x\)
Factor it out:
6x(2x + 3)
03 // NO 'C' VALUE
Factoring \(ax^2 + bx\)
When an expression has no constant term (no "c"), there is **always** an \(x\) in the GCF.
Pro Tip:
Divide each term by the GCF to find what goes inside the parentheses.
Practice 1:
x^2 + 5x = x(x + 5)
Practice 2:
3x^2 - 12x = 3x(x - 4)
Practice 3:
8x^2 + 4x = 4x(2x + 1)
04 // TRINOMIALS
Factoring \(x^2 + bx + c\)
Find two numbers that Multiply to \(c\) and Add to \(b\).
x^2 + 7x + 10
Multiply to 10
1 × 10
2 × 5
Add to 7
1 + 10 = 11
2 + 5 = 7
(x + 2)(x + 5)
Factoring Checklist
Step 1: Check for a GCF
Always look for numbers or variables that every term shares.
Step 2: Identify the Type
Is it a binomial with no constant? Or a trinomial (\(a=1\))?
Step 3: Test Your Answer
Multiply (FOIL or distribute) to see if you get the original expression back!
Factor Finding Worksheet
Factor Finding
Structural Analysis // Worksheet 01
Name:
Date:
Instructions
Break down the following expressions into their component factors. Start by identifying the Greatest Common Factor (GCF) before moving to trinomial analysis.
Phase 1: GCF Identification
Find the Greatest Common Factor (GCF) for each set of terms.
01
10x \text{ and } 15
02
6x^2 \text{ and } 8x
03
14x^3 \text{ and } 21x^2
Phase 2: Binomial Extraction
Factor out the GCF for each binomial. Ensure no common factors remain inside the parentheses.
04
x^2 + 7x
05
4x^2 - 12x
06
3x^2 + 3x
07
10x^2 - 15x
Phase 3: Trinomial Decomposition
Factor each trinomial into two binomials. Remember: Find numbers that multiply to \(c\) and add to \(b\).
08
x^2 + 8x + 12
Analysis
09
x^2 + 9x + 20
Analysis
10
x^2 - 7x + 10
Analysis
11
x^2 - 5x - 14
Analysis
12
x^2 + 3x - 10
Analysis
Phase 4: Mixed Assembly
Review each expression and apply the correct factoring technique.
13
x^2 + 11x + 24
14
x^2 - 2x - 15
15
x^2 + 6x
Standard Algebra Specification v1.0
End of Assessment
