Polynomial Factoring Calculator

Factor polynomials and algebraic expressions into their simplest form. Supports quadratic expressions and shows step-by-step solutions.

How to Use This Calculator

Enter your polynomial expression (e.g., x² + 5x + 6)
The calculator supports polynomials up to degree 2 (quadratic expressions)
Use ^ for exponents (e.g., x^2 for x²)
Click Calculate to see the factored form
The result will show the factored expression and the steps taken

Understanding Factoring

Factoring is the process of breaking down a polynomial expression into a product of simpler expressions. It's the reverse of expanding or multiplying terms. For example, x² + 5x + 6 can be factored as (x + 2)(x + 3).

Types of Factoring

Common Factor: When all terms share a common factor (e.g., 2x² + 4x = 2x(x + 2))
Difference of Squares: When the expression is in the form a² - b² (e.g., x² - 4 = (x+2)(x-2))
Perfect Square Trinomials: When the expression is a perfect square (e.g., x² + 2x + 1 = (x + 1)²)
General Trinomials: Expressions in the form ax² + bx + c (e.g., x² + 5x + 6 = (x + 2)(x + 3))

Steps in Factoring

Identify the type of expression you're dealing with
Look for common factors first
Check if it's a special pattern (difference of squares, perfect square)
For quadratic expressions (ax² + bx + c):
- Find two numbers that add to b and multiply to ac
- Use these numbers to split the middle term
- Group terms and factor by pairs

Common Mistakes to Avoid

Forgetting to check for common factors first
Not recognizing special patterns
Making arithmetic errors when finding factors
Forgetting to check your answer by expanding the factors

Enter polynomial expression

Use x^2 or x² for squared terms