11-29 Math Skills notes

Factoring turns a number or expression into a multiplication problem.

72 = 9 times 4 times 2
6x^2 = 6 times x times x


If a number's digits add up to 9, then 9 is a factor of that number.
If a number ends in 5 or 0, then 5 is a factor of that number.
If a number ends in 0, then 10, 5, and 2 are factors of that number.
If a number is even, then 2 is a factor of that number.


Factoring into pairs results in a multiplication problem with two pieces.  There may be more than one pair for an answer.

72 = 9 x 8
72 = 6 x 12
72 = 36 x 2


Factoring completely means factoring the factors until only prime number factors remain.

72 =    6     times        12
           factor the 6 and factor the 12
     = 2 x 3  times   3    x   4
                            factor the 4
     = 2 x 3  times   3 x ( 2 x 2 )
     = 2 x 3 x 3 x 2 x 2


A problem that involves factoring into possible pairs may require a specific pair for the answer because another condition, or "catch", is placed on the relationship between the factors.

Given
72 = 9 x 8
72 = 6 x 12
72 = 36 x 2
an additional condition might be that the difference between factors is 6,
or one factor minus the other factor = 6.
The only pair of factors that make this true is 6 and 12, because 12 - 6 = 6, the catch.