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.

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Presentation transcript:

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.

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. 5x 2 (x 2 – 2x + 5) 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. 2a 2 b(8b 2 – 7a 3 b – 2a 6 )

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.