Download Rules for Factoring

Rules for Factoring:
1. Factor out the GCF
(what’s the biggest number/variable you can pull out of all terms?)
Ex: 3x+ 6  3 (x +2)
Ex: 18x2 + 9x  9x (2x +1)
2. Look for the difference of 2 squares
(can you get the square root of the first term and the 2nd term, and is there a – sign in between?)
Ex: x2 -1  (x + 1) (x-1)
Ex: (4x2 – 49)  (2x + 7) (2x – 7)
3. (finish) (factoring)
( what numbers can multiply to equal the last term, but add together to equal the middle term?)
Ex: x2 – 9x + 18  ( x – 6) (x – 3)
Ex: 2 x2 +5x – 3  ( 2x - 1) ( x +3)
Rules for simplifying rational expressions:
1. Follow rules for factoring
2. look for restrictions
(what numbers would make the bottom zero if you plugged them in?)
3. cancel
(what identical parts from the top and bottom can be cancelled out?)
Ex:
( x  2)(2 x  1)
( x  2)

(2 x  1)( x  2)
( x  2)
Rules for multiplying rational expressions:
1. Follow the rules for simplifying rational expressions
2. multiply what’s left going across
(multiply top by top and bottom by bottom)
Rules for ÷ rational expressions
1. Flip the 2nd fraction and change it to multiplication
2. follow the rules for multiplying rational expressions
Rules for + and - rational expressions
1. Factor the denominators using rules for
factoring
Ex:
2x
3
3


( x  1)( x  3) 4( x  1)
x 2  2x  3 4x  4
2x

2. “Play the game” to find the common
denominator ( looking at the bottom, decide “what’s he got that I don’t?” )
this side is missing 4 ->
2x
3

( x  1)( x  3) 4( x  1)
<- this side is missing (x-3)
3. Whatever you multiplied the bottom by to
get the common denominator, you must also
multiply to the top of that fraction.
( x  3)
4
2x
3

.
.
4 ( x  1)( x  3) 4( x  1) ( x  3)
3( x  3)
8x

4( x  1)( x  3) 4( x  1)( x  3)
4. Make one fraction
(write both sides exactly as they are over one denominator, be careful distributing negatives)
8x  3( x  3)
4( x  1)( x  3)
5. “Clean up” the top, bottom is done
(distribute, combine like terms, put them in standard form)
8x  3( x  3)
--distribute - 3 to (x-3)
4( x  1)( x  3)
8 x  3x  9
5x  9
 combine like terms to get final answer 
4( x  1)( x  3)
4( x  1)( x  3)