Free Online Factoring Calculator - Accurate & Easy Math Tool
Original Expression
1x² +5x +6
Factored Form
(x - (-2.0000))(x - (-3.0000))
(x +2)(x +3)
Roots
x₁ = -2.0000
x₂ = -3.0000
Verification:
✓ Formula verified correctly
How It Works
Enter Coefficients
Input a, b, and c values
Calculate Factors
Find roots and factored form
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What is Factoring?
What
Factoring breaks down expressions into smaller pieces that multiply together. Like finding ingredients in a recipe - we find the parts that make the whole.
Why
Factoring makes solving equations much easier. Instead of working with complex expressions, we get simpler parts that are easier to understand and solve.
Uses
Solving equations, simplifying fractions, finding zeros of functions, and understanding mathematical patterns in algebra and beyond.
Simple Example:
If you have x² + 5x + 6, factoring gives you (x + 2)(x + 3). Both forms are equal, but the factored form makes it easy to see that x = -2 or x = -3 are solutions!
Common Examples
Example 1: Simple Factoring
Expression: x² + 5x + 6
Coefficients: a=1, b=5, c=6
Factored: (x + 2)(x + 3)
✓ Check: (x+2)(x+3) = x² + 5x + 6
Example 2: Negative Terms
Expression: x² - 7x + 12
Coefficients: a=1, b=-7, c=12
Factored: (x - 3)(x - 4)
✓ Check: (x-3)(x-4) = x² - 7x + 12
Example 3: Leading Coefficient
Expression: 2x² + 8x + 6
Coefficients: a=2, b=8, c=6
Factored: 2(x + 1)(x + 3)
✓ Factor out GCF first, then factor
Example 4: Mixed Signs
Expression: x² + 2x - 15
Coefficients: a=1, b=2, c=-15
Factored: (x + 5)(x - 3)
✓ One positive, one negative factor
Calculation Table
| Expression | Coefficients (a,b,c) | Factored Form | Roots |
|---|---|---|---|
| x² + 5x + 6 | (1, 5, 6) | (x + 2)(x + 3) | x = -2, -3 |
| x² - 7x + 12 | (1, -7, 12) | (x - 3)(x - 4) | x = 3, 4 |
| x² - 4 | (1, 0, -4) | (x + 2)(x - 2) | x = -2, 2 |
| 2x² + 8x + 6 | (2, 8, 6) | 2(x + 1)(x + 3) | x = -1, -3 |
| x² + 2x - 15 | (1, 2, -15) | (x + 5)(x - 3) | x = -5, 3 |
Frequently Asked Questions
What is factoring in algebra?
Factoring breaks down expressions into smaller parts that multiply together to make the original. It's like finding the ingredients in a recipe - we discover what pieces combine to create the whole expression.
How do I check if my factoring is correct?
Multiply your factors back together using FOIL (First, Outer, Inner, Last). If you get the original expression, your factoring is correct. For example: (x + 2)(x + 3) = x² + 5x + 6.
What if my expression can't be factored?
Some expressions don't factor nicely with real numbers. Our calculator will show "no real factors" when this happens. You can still solve these using the quadratic formula to find complex solutions.
Why do I sometimes get decimal factors?
Not all expressions factor into nice whole numbers. Decimal factors are perfectly valid - they just mean the roots aren't integers. This is completely normal in algebra.
When should I factor out the GCF first?
Always look for a Greatest Common Factor (GCF) first. If all terms share a common factor, pull it out before factoring the remaining expression. This makes the problem much easier to solve.