FACTORING & APPLICATIONS

6.1 The Greatest Common Factor; Factor by Grouping

FACTORING
(to ex press as a multiplication )

Step 1: Factor out GCF (greatest common factor )
Step 2:
  Count the terms
  4-terms -> grouping (2-steps)
  3-terms -> trial & error or master product
  2-terms -> difference of squares

difference of cubes

sum of cubes

FACTOR (verb): express as a multiplication

example: Factor 12

12 = 1(12) 12 = 2(6)
12 = 3(4)	note: factors of a number divide it evenly, 1,2,3,4,12 divide 12 evenly
	this is called the Prime Factorization of 12 because all the factors are prime numbers

Greatest Common Factor (GCF)

example: Find the GCF of 12 and 16……..do you know the answer??

If not…step 1: prime factor each number (tree method or division )

step 2: multiply the factors they have in common

GCF = 2^2 or 4 note: since 4 is a factor (GCF) it will divide 12 & 16 evenly

example: Find the GCF of

FACTORING

Step 1: Factor out GCF or Divide out GCF

example:

	remember (see above)
	check this answer by multiplying out and seeing if you get the original problem

FACTORING

Step 1: Factor out GCF
Step 2: Count the terms

4-terms: grouping (2-steps)

example 1:

	four terms, no GCF, we try groups of 2 factor out GCF of each group notice there is now a GCF of (x + 3)
	SO factor out (x + 3), now the expression is completely factored Look at the original addition problem , it has now been rewritten as a multiplication problem…factored!!

example 2:

The sign change in example 2 is often overlooked on the exam. Also remember
when factoring by grouping you are d one until you’ve completed 2 steps .