Introduction
This Factoring Calculator helps you break down math problems into smaller parts. You can factor polynomials, like x² + 5x + 6, or whole numbers, like 48. Just type in what you want to factor and click Calculate.
The tool shows you the answer right away. It also shows each step, so you can see how the answer was found. This makes it easy to learn and check your own work.
You can pick from many factoring methods. These include finding the greatest common factor (GCF), factoring trinomials, grouping, perfect square trinomials, difference of squares, and the sum or difference of cubes. For whole numbers, you get the prime factorization, a list of factor pairs, and more.
Whether you are doing homework or just need a quick check, this calculator gives clear answers and simple steps to help you understand factoring.
How to use our Factoring Calculator
Pick what you want to factor, type your number or expression, and the calculator shows the factored answer with clear steps.
Factoring Mode: Choose "Polynomial Factoring" to break down an expression like x² + 5x + 6, or "Integer Factoring" to find the factors of a whole number.
Factoring Method: For polynomials, pick how you want to factor, such as Factor Completely, GCF, Trinomials, Grouping, Difference of Squares, or Cubes. This shapes the steps you see.
Expression Input: Type the polynomial you want to factor. Use ^ for powers, * for multiply, and one variable like x or y. The ± button flips the sign, and the keypad helps you add symbols.
Integer Input: Type the whole number you want to factor. It can be positive or negative, up to 10 digits. The ± button switches it between positive and negative.
Calculate: Click this button to get your factored result, step-by-step solution, and a graph or factor table.
Reset: Click this button to clear your work and start over with the default values.
What Is Factoring?
Factoring means breaking a number or a math expression into smaller parts that multiply together to make the original. Those parts are called factors. For example, you can factor 6 into 2 × 3. You can factor x² + 5x + 6 into (x + 2)(x + 3). When you multiply the factors back, you get what you started with.
Factoring Whole Numbers
Every whole number can be split into smaller numbers that divide it evenly. A prime number can only be split into 1 and itself, like 7 or 13. Other numbers, called composite numbers, break down into prime factors. For example, 48 = 2 × 2 × 2 × 2 × 3. This list of primes is called the prime factorization, and it is the same for every number, no matter how you find it. You can also use the LCM Calculator to find the least common multiple of two numbers.
Factoring Polynomials
A polynomial is a math expression with terms like x², x, and plain numbers. Factoring a polynomial means writing it as factors multiplied together. There are a few common ways to do this:
- GCF (Greatest Common Factor): Pull out the biggest part every term shares. Try our GCF Calculator for whole numbers.
- Trinomials: Factor three-term expressions like x² + 5x + 6 into two sets of parentheses.
- Difference of Squares: Use the rule a² − b² = (a − b)(a + b).
- Perfect Square Trinomial: A trinomial that turns into one squared factor.
- Sum or Difference of Cubes: Special rules for terms raised to the third power.
- Grouping: Group terms in pairs to find shared factors.
For more polynomial tools, check out the Polynomial Calculator, the Synthetic Division Calculator, and the Quadratic Formula Calculator.
Why Factoring Matters
Factoring helps you solve equations, simplify fractions, and find where a graph crosses the x-axis. It is a key skill in algebra that you use again and again in higher math. Learning to factor by hand also helps you spot patterns faster. Related tools like the Vertex Calculator and Exponent Calculator can help with other algebra steps.
Tips for Good Input
For numbers, type any whole number, even a negative one. For polynomials, use ^ for powers, like x^2, and stick to one variable. The step-by-step solution shows how the answer is found, so you can check your work and learn the method too. If you need to simplify results, the Fraction Calculator and Square Root Calculator are handy companions.