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Factoring
Common Factoring Using
Algebra Tiles as a Tool and
Patterning as a Strategy
Key Points
♦  Factoring
–  The process of rewriting an expression as a
product or multiplication, (ie) putting the
brackets back in the question.
♦  Common Factoring
–  The easiest, but most important type of
factoring.
♦  Greatest Common Factor (GCF)
–  It is the largest integer that is a factor of all
of the integers.
♦  Greatest Common Monomial Factor
–  It is largest monomial that is a factor of the
polynomial.
Common Factoring Using Algebra
Tiles
♦  Represent the expression 3x+3 with algebra tiles.
♦  Place the tiles into equal groups. How many of
groups can you make? What does each group
consist of?
3 groups
x
1
x
1
x
1
Each group
has an x and
a1
Common Factoring Using Algebra
Tiles (continued)
♦ 
♦ 
♦ 
The greatest common factor is 3. The remaining
expression is (x+1).
The expression 3x+3 can be rewritten as 3(x+1).
Examples:
1. 
Factor.
a)  2x+4
= 2(x+2)
b) 5x-10
= 5(x-2)
Common Factoring Using Algebra
Tiles (continued)
♦ 
Examples (continued):
2. 
Factor each of the following fully.
a)  3x2+6x+12
= 3(x2+2x+4)
c)  2x2-8x+10
= 2(x2-4x+5)
b) 2x2+6x-8
= 2(x2+3x-4)
d) 4x2+8x+8
= 4(x2+2x+2)
Common Factoring Using
Patterning
♦  Start by examining the coefficients of
each term and find their GCF.
♦  Look at the variables of each term and find
the greatest variable term that could be
factored out.
♦  This is the GCMF, write it on the next line
after =.
♦  Put in the brackets and fill the brackets
with the leftovers (what you would have
to multiply the GCMF by to expand the
original question).
Common Factoring Using
Patterning (continued)
♦ 
Examples
1. 
Factor.
a) 
12a+18
= 6(2a+3)
c) 49k5-35k4-7k3
= 7k3(7k2-5k-1)
e) 12x2y+16xy
= 4xy(3x+4)
g) 4x2-8x+12
= 4(x2-2x+3)
b) 7w3-3w2+4w
= w(7w2-3w+4)
d) 15n-24
= 3(5n-8)
f) 5m2n2-10mn2+25m2n
= 5mn(mn-2n+5m)
h) 25x2+30x-55
= 5(5x2+6x-11)
Homework
♦  Worksheet