Factoring is the process of breaking down a mathematical expression or number into smaller components (factors) that, when multiplied together, give the original number or expression. For numbers, it involves finding integers that divide the number evenly. For polynomials, it means finding two or more binomials whose product is the polynomial.

What is the difference between factoring numbers and factoring polynomials?

Factoring numbers (e.g., 12 = 2² * 3) is about finding the prime factors. Factoring polynomials (e.g., x² - 4 = (x-2)(x+2)) is about finding the simpler expressions (binomials) whose product is the original polynomial. Polynomial factoring is a core skill in algebra.

Factoring Calculator (Quadratic Polynomials)

Q: When should I use the factoring calculator?

You should use the calculator to: 1. Factor trinomials (Ax² + Bx + C) to find their roots (solutions). 2. Check your work when using the grouping method or the quadratic formula. 3. Find the Greatest Common Factor (GCF) or prime factorization of integers.

Factor any quadratic equation in the form **Ax² + Bx + C = 0**. Our tool provides the fully factored form and the step-by-step solution using the grouping method.

Quadratic Factoring ($Ax^2 + Bx + C$)

Factors of a Single Integer

Enter an Integer:

All Factors (Divisors)

Prime Factorization

What is Factoring in Math?

Factoring is one of the most essential skills in algebra. It is the process of breaking down a complex expression (like a polynomial) into a product of simpler terms. When you factor a polynomial, you are essentially finding the binomials that, when multiplied together, result in the original expression.

Key Factoring Methods (Polynomials)

Greatest Common Factor (GCF): The first step for any expression. You factor out the largest term that all parts of the polynomial share (e.g., $3x^2 + 6x = 3x(x+2)$).
Factoring Trinomials ($Ax^2 + Bx + C$): The grouping method (sum-product) is the most common technique taught to students. You split the middle term ($Bx$) into two terms ($Mx + Nx$) such that $M \times N = A \times C$ and $M + N = B$.
Difference of Squares: A special case where $a^2 - b^2 = (a - b)(a + b)$ (e.g., $x^2 - 9 = (x-3)(x+3)$).

Our calculator primarily uses the grouping method to factor polynomials of the form $Ax^2 + Bx + C$.

Factoring Numbers vs. Factoring Expressions

While the goal is the same—to find the parts that multiply back to the original—the application is different:

Factoring Numbers: Leads to the Prime Factorization (the set of prime numbers that multiply to the original number, e.g., $24 = 2^3 \cdot 3$).
Factoring Polynomials: Leads to the roots (solutions) of the equation. If $(x+3)(x+2)=0$, the roots are $x=-3$ and $x=-2$.

Frequently Asked Questions (FAQ)

What is the easiest way to factor a quadratic equation?

The easiest way is often the **grouping (sum-product) method** for trinomials ($A=1$). For any quadratic, the fastest way to find the factors (roots) is by using the **Quadratic Formula** ($x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$), which can then be used to write the factored form.

When should I use the factoring calculator?

You should use the calculator to: 1) Practice the grouping method and verify your M and N numbers. 2) Check the final factored form of a homework problem. 3) Find the prime factorization of very large numbers.