THE FIRST RULE OF FACTORING IS TO FACTOR OUT THE GCF
Factoring Trinomials of the Type x 2  bx  c
--answer will always be the product of 2 binomials
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If c is positive:
 Look for factors of c whose sum is b
 Signs in binomials will match the sign of b
If c is negative:
 Look for factors of c whose difference is b
 Higher factor will have same sign as b
 Smaller factor will have opposite sign of b
Factoring Trinomials of the Type ax 2  bx  c
--answer will always be the product of 2 binomials
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List factors of a in ONE order
List factors of c in BOTH orders
Write lists next to each other  a a c c 
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Multiply outer factor times outer factor and inner factor times inner factor
Follow rules of positive vs negative c to see if add or subtract those products
Factoring Special Cases
Perfect Square Trinomial with a  1
If ‘c’ is a perfect square, find c and see if 2  c gets you ‘b’
Perfect Square Trinomial with a  1
If ‘a’ & ‘c’ are perfect squares, find
Difference of 2 Squares
a 2  b 2   a  b a  b
a and
c ; see if 2  a c gets you ‘b’
1) r 2  4r  3
2) k 2  5k  6
3) x 2  2 x  1
4) y 2  16 y  28
5) y 2  y  20
6) p 2  15 p  54
7) t 2  10tw  75w2
8) 2 y 2  5 y  2
9) 6n 2  23n  7
10) 2q 2  11q  21
11) 2n 2  15n  7
12) 54 p 2  87 p  28
13) 36 f 2  114 f  20
14) h 2  12h  36
15) k 2  16k  64
16) 4m2  20m  25
17) 25 p 2  40 p  16
2
18) x  64
19) 4 y 2  81
20) 64r 2  144r  81
21) x 2  256
22) 3m2  12
23) 3y 2  48 y  192