Factoring Calculator Step by Step

Factoring Methods:

Common methods include:

Greatest Common Factor (GCF)
Grouping
Difference of Squares
Trinomial Factoring
Sum/Difference of Cubes

Factored Form:

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1. What is Factoring?

Factoring is the process of breaking down an algebraic expression into simpler parts (factors) that when multiplied together give the original expression. It's a fundamental skill in algebra used for simplifying expressions and solving equations.

2. Common Factoring Methods

The main factoring techniques include:

GCF (Greatest Common Factor): Factor out the largest common term
Grouping: For 4-term polynomials, group terms in pairs
Difference of Squares: \( a^2 - b^2 = (a-b)(a+b) \)
Trinomial Factoring: \( x^2 + bx + c = (x+m)(x+n) \) where m×n=c and m+n=b
Sum/Difference of Cubes: Special formulas for cubic terms

3. Step-by-Step Process

General Approach:

Look for GCF in all terms
Identify number of terms and pattern
Apply appropriate factoring method
Check by multiplying factors back
Repeat until expression is fully factored

4. Using the Calculator

Tips: Enter algebraic expressions using ^ for exponents (e.g., x^2 for x²). The calculator will show the factored form and step-by-step process.

5. Frequently Asked Questions (FAQ)

Q1: What's the first thing to look for when factoring?
A: Always start by checking for a Greatest Common Factor (GCF) in all terms.

Q2: How do I factor trinomials?
A: For x²+bx+c, find two numbers that multiply to c and add to b.

Q3: What if an expression can't be factored?
A: Some expressions are "prime" and cannot be factored further over the integers.

Q4: Does order matter in the factored form?
A: No, (x+2)(x+3) is the same as (x+3)(x+2) by the commutative property.

Q5: How is factoring used in solving equations?
A: After factoring, you can set each factor equal to zero to find solutions.