Factors Extension #2

 

Factor Pairs are two numbers that, when multiplied together, provide you with your desired number.

 

EXAMPLE: (2)(6) = 12, so  2 and 6 are a factor pair of 12.

 

The same is true with representations where we don’t know the actual value of the number, but only that it represents a number.

 

EXAMPLE:  (3x)(y) = 3xy, so 3x and y are a factor pair of 3xy.

 

 

The same is true with polynomials in general. Polynomials are numbers that have more than one element….

2x+5 ( a binomial – having TWO parts)    x² + 3x + 1 (a trinomial – THREE parts)

 

While there are many ways to factor polynomials, we will look at the most fundamental – factoring out what each element has in common.

 

EXAMPLE:     3x + 6 ……. What do these two parts have in common?  How about 3?

                        (3)(x)+ (3)(2)    See… so divide out the three, and turn this addition

                                                            problem into a multiplication problem

                        (3) ( x + 2)       Divide the three to the OUTSIDE and leave the remainders

                                                            on the inside

                                                So, the factors for 3x + 6 that you found are 3  and (x+2)

EXAMPLE:    4t + td

                        (4)(t) + (t)(d) =    (t) (4 + d)   …. Factors found are t and (4+d)

 

Here, you factor out a number that contains more than just a value or a variable

EXAMPLE:     12ak + 8 vk

                        (4)(3)(a)(k) + (4)(2)(v)(k) =   (4k) (3a + 2v)  factors 4k and (3a + 2v)

 

 

Factor these polynomials into two factor pairs.

1)         2w + 8                         2)         16 – 4p                        3)         ac + ah

 

 

 

 

4)         10 + 15g                      5)         3a + 6b                        6)         7c – 14

 

 

 

 

7)         abc – adb                     8)         2a + 10c – 6zd             9)         8ac – 20af + 4fc