Factoring Calculator
Factor quadratic equations step-by-step with this free factoring calculator. Enter your equation and get the factored form along with a detailed solution process.
Solution Steps
Enter an equation above and click "Factor" to see the solution steps here.
Factored Form: (x+2)(x+3)
Quadratic Equation Information
| Standard Form | x² + 5x + 6 = 0 |
|---|---|
| Factored Form | (x + 2)(x + 3) = 0 |
| Roots/Solutions | x = -2, x = -3 |
| Vertex | (-2.5, -0.25) |
| Discriminant | 1 (Two real roots) |
About Factoring Calculator
The Factoring Calculator transforms complex expressions into a product of simpler factors. It can factor expressions with polynomials involving any number of variables as well as more complex expressions.
How Factoring Works
Factoring is the process of breaking down an expression into simpler terms (factors) that when multiplied together produce the original expression. For quadratic equations, the standard form is:
ax² + bx + c = 0
The factored form is:
a(x - r₁)(x - r₂) = 0
Where r₁ and r₂ are the roots of the equation.
Common Factoring Methods
Our calculator uses several methods to factor expressions:
- Greatest Common Factor (GCF): Factor out the largest common factor from all terms
- Difference of Squares: a² - b² = (a + b)(a - b)
- Trinomial Factoring: Find two numbers that multiply to ac and add to b
- Perfect Square Trinomial: a² ± 2ab + b² = (a ± b)²
- Sum/Difference of Cubes: a³ ± b³ = (a ± b)(a² ∓ ab + b²)
Why Factor Quadratic Equations?
Factoring is a crucial skill in algebra because:
- It simplifies complex expressions
- It helps find roots/solutions to equations
- It's essential for solving higher-degree polynomials
- It's used in calculus for partial fractions and limits
- It has applications in physics, engineering, and economics
Examples of Factored Equations
| Standard Form | Factored Form |
|---|---|
| x² + 5x + 6 | (x + 2)(x + 3) |
| x² - 9 | (x + 3)(x - 3) |
| 2x² - 5x - 3 | (2x + 1)(x - 3) |
| x² + 6x + 9 | (x + 3)² |