 Millhouse squared the numbers 2 and 3, and then added 1 to get a sum of 14. ◦ = 14  Lisa squared the numbers 5 and 6, and then added 1 to get a sum of 62. ◦ = 62  14 and 62 are both divisible by 2, thus the greatest common factor of 14 and 62 is 2.

 A FACTOR is a number that can be expressed as a product of two or more numbers ◦ e.g. a factor of 9 is 3 ◦ a factor of 10 is 2; another factor is 5  The Greatest Common Factor is the largest factor that is common to two numbers ◦ EX. What is the greatest common factor of 15 and 100?  Factors of 15: 1, 3, 5, 15  Factors of 100: 1, 2, 4, 5, 10, 20, 25, and 5 are common factors, but the greatest common factor is 5.

 EX. Simplify the following expression by factoring: ◦ 12 – 27 ◦ What is common to both terms? 3. ◦ We divide out 3 from both terms ◦ 3(4 – 9) ◦ 3(-5) ◦ -15

 If you were asked to simplify an algebraic expression, you would do the same thing  EX. Factor 3x 2 – 6x ◦ What is common to both? 3 and x; divide out 3 first: ◦ 3(x 2 – 2x) ◦ Now we can divide out x as well: ◦ 3x(x – 2)  So, starting with the polynomial 3x 2 – 6x, we found its factors to be 3x and (x-2).

 EX. Factor the following expressions.  a) 10a 3 – 25a 2 ◦ The GCF to both terms is 5a 2, so divide it out ◦ 5a 2 (2a – 5)  b) 9x 4 y x 3 y 2 – 6x 2 y 3 ◦ The GCF of all 3 terms is 3x 2 y 2, so divide it out ◦ 3x 2 y 2 (3x 2 y 2 + 4x – 2y)

 EX. Factor the expression.  5x(x-2) – 3(x-2)  (x-2) is common to both terms, so factor it out  (x-2)(5x-3)

 Factoring is the opposite of expanding ◦ Expanding – multiplying ◦ Factoring – dividing  One way to factor an algebraic expression is to look for the greatest common factor (GCF) of the terms in the expression