Factoring Calculator
Solve Integers and Polynomials with our Factoring Calculator Instantly. Get step-by-step factoring solutions for quadratic polynomials and algebraic expressions.
Universal Factoring Calculator
Enter an Integer (e.g., 120) or a Polynomial (e.g., x^2 + 5x + 6)
Result
IntegerUniversal Factoring Calculator: Solve Integers & Polynomials Instantly
Use this Universal Factoring Calculator tool to solve two of the most common problems in arithmetic and algebra. This smart calculation tool allows you to input 1. integers (to find divisors and prime lists) and 2. algebraic expressions (to break down polynomials).
How to Use This Universal Factoring Calculator?
We have designed the interface to be intuitive and powerful. Follow these simple steps:
- For Numbers: Simply type a whole number (e.g., "120" or "48") into the input box. Our calculator will generate 1. the Prime Factorization, 2. a full list of Factors, and 3. Factor Pairs.
- For Algebra: Just type your expression (e.g., "x^2 + 5x + 6") using your keyboard or the on-screen math pad. Then our calculator will identify the expression and break it down into its binomial factors (e.g., "(x+2)(x+3)").
- Review Results: Click "Calculate" to see the solution. For integers, you will see a text-based factor tree. And for algebra, you will see the steps taken to reach the solution.
Formulas and Methods We Used in This Calculator
1. Integer Factoring
To factor an integer, this calculator uses the Fundamental Theorem of Arithmetic. It performs trial division to find all "prime numbers" that divide the input exactly. It then combines these primes to find all possible factor pairs.
2. Quadratic Factoring
For expressions in the format ax² + bx + c, our calculator utilizes the AC Method or grouping method. It looks for two numbers that:
- Multiply together to give the product of a and c.
- Add up to give the value of b.
Examples
Example 1: Integer Analysis
Input: 120
Prime Factors: 2 × 2 × 2 × 3 × 5
Factor Pairs: (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), (10, 12)
Example 2: Polynomial Factoring
Input: x^2 + 5x + 4
Goal: Find two numbers that add up to 5 and multiply to 4.
Result: (x + 1)(x + 4)
Frequently Asked Questions
Can this Factoring Calculator handle negative numbers?
Yes. If you input a negative integer, our calculator will include -1 as a factor.
For algebraic expressions with negative coefficients (e.g., x^2 - 5x + 6), it will correctly calculate the signs in the binomial factors.
What is the difference between a Prime Factor and a Factor Pair?
A Prime Factor is a number that can only be divided by 1 and itself (like 2, 3, 5). A Factor Pair consists of two numbers that, when multiplied, equal your original number (like 4 × 30 = 120).