WHAT TO DO:

HOW TO DO IT:

1. Now consider the trinomial with last
sign  Two numbers with a product of
15 and difference of 2 are 5 and 3

1. x^{ 2} + 2x  15 
The larger gets the "middle
sign" + Rewriting the terms to factor by grouping:

x^{ 2} + 5x  3x + 15 
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.
Watch the sign of the second group.


Factor out the common factor 
(x + 5)(x  3) Answer 
Check by multiplying back
out by FOIL method.
First  Outer  Inner  Last
Note OI terms.


2. Consider the trinomial with last sign
" +" Two numbers with a product of and sum of are


Rewriting the terms to factor by
grouping: 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 Answer 

Check by multiplying back out by FOIL
method.
First  Outer  Inner  Last
Note OI terms.


Consider the trinomial of degree 6 with
middle term degree 3 The last sign is  , two numbers
with a product of 18 and difference of 7 are 9 and 2

x^{ 6}  7x^{ 3}  18 
The larger gets the "middle
sign" "  " 

Rewriting the terms to
factor by grouping: 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.
Watch the sign of the second group.


Factor out the common factor ( x^{ 3}  9 ) 
Answer (x^{ 3}  9)(x^{ 3} + 2) 
Check by multiplying back out by FOIL method.
First  Outer  Inner  Last
Note O  I terms.

