1. What Is Factoring?

Factoring is the process of breaking down an expression into a product of simpler expressions (factors). The general form is: factored = common_factor × remaining_terms.

2. How Factoring Works

The factoring process follows this basic formula:

Where:

• \( common\_factor \) — The greatest common factor of all terms
• \( remaining\_terms \) — What's left after dividing each term by the common factor

Example: For 3x + 6, the common factor is 3, giving 3(x + 2).

3. Importance of Factoring

Details: Factoring simplifies expressions, helps solve equations, and is fundamental in algebra. It's used in polynomial division, finding roots, and simplifying complex expressions.

4. Using the Calculator

Tips: Enter the original expression and the common factor you want to extract. The calculator will show the factored form and remaining terms.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between factoring and expanding?
A: Factoring writes an expression as a product of factors, while expanding does the opposite - multiplies out factors to create a sum.

Q2: How do I find the greatest common factor?
A: For numbers, find the largest number that divides all coefficients. For variables, take the lowest power of each variable present in all terms.

Q3: Can all expressions be factored?
A: Not all expressions can be factored over the integers, but many can be factored if you allow complex numbers or irrational coefficients.

Q4: What's the difference between factoring and solving?
A: Factoring prepares an expression for solving. After factoring, you can set each factor equal to zero to find solutions.

Q5: Are there special factoring patterns?
A: Yes, including difference of squares (a² - b²), perfect square trinomials, and sum/difference of cubes.