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FACTORING

FACTORING. 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:

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FACTORING

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  1. FACTORING

  2. 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.

  3. 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.)

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

  5. Factoring Simplifying

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

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

  8. The Process of Factoring 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.

  9. GCF 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 16x2 and 12x? The biggest number that goes into 12 and 16 is 4. The biggest thing x2 and x are divisible by is x. The GCF is 4x.

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

  11. Factoring out the GCF Factor Find the GCF GCF = 5x2 2. Pull out the GCF 5x2(____ - ____ + ____) 3. Divide each term by the GCF to fill in the parentheses. 5x2(x2 – 2x + 5) Distribute to check your answer.

  12. Factoring out the GCF Factor Find the GCF GCF = 2a2b 2. Pull out the GCF 2a2b(____ - ____ + ____) 3. Divide each term by the GCF to fill in the parentheses. 2a2b(8b2 – 7a3b – 2a6)

  13. Factoring out the GCF Factor 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.

  14. Factoring out the GCF Factor 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.

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

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

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