WHAT TO DO: 
HOW TO DO IT: 
Given general trinomial of type that has
no common factor. Read the "clues of the
signs". [Read Â± as + or  ]


The constant c is the grouping
number 
GN = c 
Find all possible factors of GN = c whose
sum or difference is b
(depending on the sign before c .)
+ sum or
 difference

c = r Â· s , r > s (r + s) = b
(r  s) = b

1. Consider the trinomial : x^{ 2}
 5x + 6 The leading coefficient is 1 and the last
sign is +
The factors of 6 with a sum of 5 are 3 and 2
Since the last sign is + the "same sign" in
both binomials is  (the sign of the middle term).
Factor by grouping. Bring down the middle sign.
Complete the factors.

1. x^{ 2}  5x + 6 r Â· s = 6
and r + s = 5

2. First, examine the trinomial to see
if it has a common factor(s) in each term. Check the
remaining trinomial to see if it will factor: 
2. 3x^{ 2} +15x + 12 3(x^{
2} + 5x + 4)

2a) Consider the trinomial :
x^{ 2} + 5x + 4 The leading coefficient is 1
and the last sign is + The factors of 4 with a sum of 5
are 4 and 1 Since the last sign is + the "same
sign" in both binomials is + (the sign of the middle
term).
Factor by grouping. Bring down the middle sign.
Complete the factors.

2a) x^{ 2} + 5x + 4 r
Â· s = 4 and r + s = 5

2b) Go back to the
polynomial in the previous step: Replace the polynomial
with the factors to find all of the factors: 3x^{ 2}
+15x + 12 
2b) 3(x^{ 2} + 5x +
4) = 3(x + 1)(x + 4)

3. Consider the trinomial
with last sign + Two numbers with a product of 14 and
sum of are 7 and 2
Rewriting the terms to factor by grouping:

3. x^{ 2} + 9x + 14 x^{
2} + 7x + 2x + 14

Then group the terms 2 Ã— 2
into two terms. Factor common factors. Bring down the
middle sign.
Find the common factor for each group.


Factor out the common factor 
(x + 7)(x + 2) Answer 
Check by multiplying back out by 
F 0 I L 
FOIL method. First  Outer  Inner 
Last
Note OI terms.

