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### Identifying Prime Numbers

A prime number is a whole number larger than the number 1 that can be divided evenly *only* by itself and 1. The first and smallest prime number is the number 2. It’s the only even prime number. All primes [more…]

### How to Write Prime Factorization of Composite Numbers

Prime factorization shows you the only way a number can be factored. The process of prime factorization breaks down a composite number into the prime numbers that, when multiplied together, give you that [more…]

### How to Reduce Fractions Using Prime Factorization

You can use prime factorization to reduce fractions. Start with numbers only and then add variables (letters that represent any real number) to the mix. The beauty of using the prime factorization method [more…]

### How to Factor Out Numbers

Factoring is the opposite of distributing. When distributing, you multiply a series of terms by a common factor. When factoring, you seek to find what a series of terms have in common and then take it [more…]

### How to Factor Out Variables

You can factor out variables from the terms in an expression. You factor out variables the same way as you do numbers *except* that when you factor out powers of a variable, the [more…]

### Factoring Binomials

If a binomial expression can be factored at all, it must be factored in one of four ways. To decide which way you will use, you first look at the addition or subtraction sign that always separates the [more…]

### How to Factor the Sum of Two Perfect Cubes

The rule for factoring the sum of two perfect cubes is almost the same as the rule for factoring the difference between perfect cubes. You just have to change two little signs to make it work. The sum [more…]

### How to Factor the Difference of Two Perfect Squares

If two terms in a binomial are perfect squares separated by subtraction, then you can factor them. To factor the difference of two perfect squares, remember this rule: if subtraction separates two squared [more…]

### How to Factor the Difference of Two Perfect Cubes

To factor the difference of two perfect cubes, remember this rule: the difference of two perfect cubes equals the difference of their cube roots multiplied by the sum of their squares and the product of [more…]

### How to Group Six Terms for Factoring

You can group terms for factoring in expressions where the terms don't share a common factor or common variable. When grouping six terms for factoring, there’s the chance that the groups can be two groups [more…]

### Algebra's Rules of Divisibility

In algebra, knowing the rules of divisibility can help you solve faster. When factoring algebraic expressions to solve equations, you need to be able to pull out the greatest factor. You also need common [more…]

### Factoring Special Problems

Binomials, their powers, and their products with selected trinomials occur frequently in algebraic processes. By using the patterns shown here, you save time and reduce the opportunity for errors. [more…]

### Factoring in Algebra I

Factoring algebraic expressions is one of the most important techniques you need to practice. Not much else can be done in terms of solving equations, graphing functions and conics, and working on math [more…]

### Digging Up Polynomial Roots with Factoring

When solving for roots (*x*-intercepts of a polynomial), you usually need to factor the function rule and set it equal to 0. The factorization can be simple and obvious or complicated and obscure. You always [more…]

### How to Simplify Factorial Expressions

Sets of elements have special operations used to combine them or change them. Another operation that’s used with sets (but that isn’t exclusive to sets) is [more…]