To factor means to write a number or expression as a product of primes. In other words, to write a number or expression as things being multiplied together. The things being multiplied together are called factors.

 Here is a simple example of factoring: The factors are 2, 2 and 3 which are all prime numbers. (They are only divisible by themselves and 1.)

Factoring is the opposite of simplifying. To go from (x+3)(x-6) to you simplify. To go from to (x+7)(x-2) you factor.

Simplifying Factoring

Simplified. No parentheses and no like terms. Factored. A product of primes.

Factored. A product of primes. There are 4 factors. Simplified. No parentheses and no like terms.

The first thing you always do when factoring is look for a greatest common factor. GCF GCF: the biggest number or expression that all the other numbers or expressions can be divided by.

What is the GCF of 27 and 18? The biggest number they are both divisible by is 9 so the GCF is 9. What is the GCF of 16x 2 and 12x? The biggest number that goes into 12 and 16 is 4. The biggest thing x 2 and x are divisible by is x. The GCF is 4x. ** If all the terms contain the same variable, the GCF will contain the lowest power of that variable.

Factoring out or pulling out the GCF is using the distributive property backwards. Distribute 3x factor out 3x

Factor 1.Find the GCF GCF = 5x 2 2. Pull out the GCF 5x 2 (____ - ____ + ____) 3. Divide each term by the GCF to fill in the parentheses. Distribute to check your answer.

Factor 1.Find the GCF GCF = 2a 2 b 2. Pull out the GCF 2a 2 b(____ - ____ + ____) 3. Divide each term by the GCF to fill in the parentheses.

Factor 1.Find the GCF GCF = (x + 5) 2. Pull out the GCF (x + 5)(_____ - _____) 3. Divide each term by the GCF to fill in the parentheses.

Factor 1.Find the GCF HMMMM? These two terms do not have a common factor other than 1! If an expression can’t be factored it is prime.

You try: Factor 1.Find the GCF 2. Pull out the GCF 3. Divide each term by the GCF to fill in the parentheses. Better written as-

You try: Factor 1.Find the GCF 2. Pull out the GCF 3. Divide each term by the GCF to fill in the parentheses.

Factoring Binomials (2 Terms)

Remember: The first thing you always do when factoring is pull out a GCF if possible. If there is a GCF and you have factored it out you then look to see if there is any other factoring that can be done.

A sum or difference of cubes involves two terms that are both perfect cubes. The operation between them can be addition or subtraction. When you have to factor an expression with two terms it could be a difference of squares or a sum or difference of cubes. A difference of squares involves two terms that are both perfect squares and subtraction.

perfect square – perfect square Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169… If a variable has an even exponent then it is a perfect square. Difference of Squares

You factor a difference of squares using the following rule: Difference of Squares A difference of squares factors as binomial conjugates. There will be two binomial factors containing the same terms but one will be addition and one will be subtraction.

Factor: addition subtraction Check your answer by FOILing!

Sum of cubes and difference of cubes are both binomials. Both terms are perfect cubes. perfect cube + perfect cube or perfect cube – perfect cube Perfect cubes: 1, 8, 27, 64, 125… or any variable with an exponent divisible by 3. Sum and Difference of Cubes

A sum or difference of cubes will have two factors. One is a binomial the other is a trinomial. Sum and Difference of Cubes

Factor a sum or difference of cubes using the following rule: Notice the terms in the binomial factor are the cubed root of the terms in the original problem and the sign is the same. You can remember this by remembering CSC (cubed root, same sign, cubed root)

Notice the first and last terms in the trinomial factor are the square of the terms in the binomial factor. Notice that the middle term in the trinomial factor is the product of the two terms in the binomial factor.

Notice that the first sign in the trinomial factor is the opposite of the sign in the binomial factor. Notice that the last operation is always addition.

So, you can remember what goes in the binomial factor by remembering CSC ( C ubed root, S ame sign, C ubed root)

To remember what goes in the trinomial factor just remember SOPAS P roduct, O pposite sign, S quare, S quare A dd,