Factoring Calculator - Factor Polynomials, Quadratics, GCF | 8gwifi.org

Factoring Calculator

Factor polynomials, quadratics, and algebraic expressions with step-by-step solutions

Enter Expression to Factor
Factor quadratic expressions:
ax² + bx + c format
Examples:
• x² + 5x + 6 → enter a=1, b=5, c=6
• 2x² - 8x + 6 → enter a=2, b=-8, c=6
• x² - 9 → enter a=1, b=0, c=-9
Special factoring patterns:
Difference of squares, perfect squares, sum/difference of cubes
Enter the coefficient (e.g., 16 for 16x²)
Enter the coefficient (e.g., 9 for 9)
Examples:
• x² - 25 → Difference of Squares
• x² + 6x + 9 → Perfect Square
• x³ + 8 → Sum of Cubes
Enter any polynomial expression:
Supports GCF extraction and basic factoring
Use ^ for exponents: x^2, 2*x^3, etc.
Examples:
• 3x^2 + 12x + 9
• 2x^3 - 8x
• x^3 - 27
Factoring Methods
1. Greatest Common Factor (GCF)

Always factor out GCF first!

GCF(12x³ + 18x²) = 6x² · (2x + 3)
2. Quadratic Trinomials (ax² + bx + c)

Method 1: Simple (a = 1): Find two numbers that multiply to c and add to b

x² + 5x + 6 = (x + 2)(x + 3)

Method 2: AC Method (a ≠ 1):

  1. Multiply a × c
  2. Find two numbers that multiply to ac and add to b
  3. Split middle term and factor by grouping
2x² + 7x + 3 = 2x² + 6x + x + 3
= 2x(x + 3) + 1(x + 3) = (2x + 1)(x + 3)
3. Special Products

Difference of Squares:

a² - b² = (a + b)(a - b)

Example: x² - 25 = (x + 5)(x - 5)

Perfect Square Trinomial:

a² + 2ab + b² = (a + b)²
a² - 2ab + b² = (a - b)²

Example: x² + 6x + 9 = (x + 3)²

Sum of Cubes:

a³ + b³ = (a + b)(a² - ab + b²)

Difference of Cubes:

a³ - b³ = (a - b)(a² + ab + b²)
4. Factor by Grouping

For 4-term polynomials:

ax + ay + bx + by = a(x + y) + b(x + y)
= (a + b)(x + y)
Factoring Strategy
  1. GCF: Factor out greatest common factor first
  2. Count terms:
    • 2 terms → Check for difference of squares or sum/difference of cubes
    • 3 terms → Check for perfect square trinomial, then factor as quadratic
    • 4+ terms → Try factoring by grouping
  3. Check: Multiply factors to verify
  4. Factor completely: Continue until all factors are prime
Factored Form

Enter an expression and click factor to see the result

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