How to Factor
Learn how to factor numbers and basic algebra expressions with common factors, factor pairs, examples, mistakes, troubleshooting, and FAQs.
Quick Answer
To factor, rewrite a number or expression as smaller parts that multiply to make the original. For numbers, list factor pairs. For algebra, first look for the greatest common factor, then use patterns such as difference of squares or trinomials when they apply.
What You Need
- Pencil
- Paper
- Multiplication facts
- Expression or number to factor
- Basic exponent rules
Safety Precautions
- Check factors by multiplying them back together.
- Look for the greatest common factor first.
- Keep signs attached to terms.
- Do not assume every expression factors neatly with integers.
- Write each step clearly to avoid sign errors.
Step-by-Step Instructions
- Step 1
Identify what you are factoring
Decide whether it is a whole number, monomial, binomial, or trinomial.
- Step 2
Find factor pairs
For numbers, list pairs that multiply to the original number.
- Step 3
Look for a GCF
For expressions, pull out the greatest common factor shared by all terms.
- Step 4
Check patterns
Look for common patterns such as difference of squares.
- Step 5
Factor trinomials
Find two numbers that multiply to the constant term and add to the middle coefficient when applicable.
- Step 6
Multiply back
Expand your factors to confirm they produce the original expression.
- Step 7
Stop when complete
If no smaller integer factors remain, the expression is fully factored for your class level.
Practical Example
Example: To factor 6x + 12, the greatest common factor is 6, so the factored form is 6(x + 2).
Common Mistakes
- Skipping the greatest common factor
- Dropping negative signs
- Guessing without checking
- Forgetting to factor all terms
- Over-factoring prime numbers
- Not multiplying back
Troubleshooting
I do not know where to start
Look for the greatest common factor before trying other patterns.
Signs keep coming out wrong
Write factor pairs with their signs and check by multiplication.
A trinomial will not factor
It may not factor over integers, or you may need a different method.
Answer differs from the key
Multiply both forms out; equivalent factors can look different.
Helpful Internal Links
FAQs
What does factor mean?
A factor is something that multiplies with another factor to make a number or expression.
What is the greatest common factor?
It is the largest factor shared by all the terms or numbers you are working with.
How do I check factoring?
Multiply the factors back together. You should get the original number or expression.
Can every expression be factored?
Not every expression factors neatly over whole numbers or integers.
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