1. Factoring Summary To factor something means…
to break it down into parts that will multiply to equal what is being factored
or …to find the sides of a rectangle
e.g
= (2)(3)
e.g x + 8
= 4(x+2)
e.g x x +6
= (x +2)(x +3)

2. The following types of factoring have been studied:
Factoring Summary
The following types of factoring have been studied:
Name
Example
Solution Methods
Common
4x + 8
= 4(x+2)
Model/Draw with Alge tiles (i.e. rectangles and groups) Use Rules/Procedures developed (i.e. factor out the g.c.f.)

3. The following types of factoring have been studied:
Factoring Summary
The following types of factoring have been studied:
Name
Example
Solution Methods
Common
4x + 8
= 4(x+2)
Model/Draw with Alge tiles (i.e. rectangles and groups) Use Rules/Procedures developed (i.e. factor out the g.c.f.)
Trinomials of the form
1x 2 + bx + c
x x +6
=(x +2)(x +3)
Model/Draw with Alge tiles (i.e. rectangles) Use Rules/Procedures developed
x 2 + bx + c = (x + ?)(x + ?) determine the constants that x to = c
and + to = b

4. The following types of factoring have been studied:
Factoring Summary
The following types of factoring have been studied:
Name
Example
Solution Methods
Common
4x + 8
= 4(x+2)
Model/Draw with Alge tiles (i.e. rectangles and groups) Use Rules/Procedures developed (i.e. factor out the g.c.f.)
Trinomials of the form
1x 2 + bx + c
x x +6
=(x +2)(x +3)
Model/Draw with Alge tiles (i.e. rectangles) Use Rules/Procedures developed
x 2 + bx + c = (x + ?)(x + ?) determine the constants that x to = c
and + to = b
ax 2 + bx + c
2x x +6
=(2x +3)(x +2)
Model/Draw with Alge tiles (i.e. rectangles) Trial and Error Use Rules/Procedures developed Decomposition
ax 2 + bx + c = ax 2 + dx + ex + c replace bx with dx and ex
such that de = ac and d + e = b,
then common factor fully

5. Factoring Summary When asked to factor a polynomial :
common factor first, if possible
if there is a common factor and the polynomial is common factored check the factor in the brackets to see if it can be factored
if there is no common factor, factor it using methods for trinomials (1x 2 + bx + c or ax 2 + bx + c)

6. Examples a) 4x + 6
=2(2x + 3) common
the factor in brackets can’t be factored
b) 3x 2 – 9x -30
=3( x 2 – 3x -10) common
factor the polynomial/factor in the brackets
= 3 (x -5)(x +2)
c) x 2 – 9x + 20
no common factor, use methods for 1x 2+bx+c
= (x – 4)( x – 5)
d) 2x 2 + 5x + 2
no common factor, use methods for ax 2+bx+c
= (2x + 1)(x + 2)