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Factoring – Greatest Common Factor
REVIEW TYPES OF FACTORING
1. Trinomial
Factoring
i.e. x2 + 8x + 12
2. Perfect Square
Trinomial
i.e. x2 – 10x + 25
Find two numbers that multiply to 25 and add to -10.
= (x – 5)(x – 5)
Since the two brackets are the same, write it as
= (x – 5)2
squared
i.e. x2 – 121
Take the square root of each term
= (x + 11)(x – 11)
The square root can be a positive or negative number
3. Difference of
Squares
Find two numbers that multiply to 12 and add to 8
= (x + 2)(x + 6)
GREATEST COMMON FACTOR (x2 + bx)
Method 1
Rewrite the Polynomial in the form x2 + bx + c
c
 Find two numbers that multiply to ______
and
b
add to _______
i.e. x2 + 5x = x2 + 5x + 0 in this case c = 0
= x2 + 5x + 0
= (x + 0)(x + 5)
= x (x + 5)
EXAMPLES
1. x2 + 15x
= x(x + 15)
find 2 numbers that multiply
to zero and add to 5
Method 2
Find the Greatest Common Factor

factor
The largest ___________
by which you can
divide
______________
ALL terms in a polynomial
x
i.e. x2 + 5x GCF = _______
= x2 + 5x remove one x from each term, as it is
common
= x (x + 5)
2. 4x2 – 8
= 4(x2 – 2)
3. 3x2 + 18x
= 3x(x + 6)
FULLY FACTORING TRINOMIALS of the FORM ax2 +bx + c
4x2 – 8x – 60
= 4(4x2 – 8x – 60)
4
4
4
GCF = 4
first pull out the GCF and divide
each term by it
Steps to Fully Factoring (in this order)
= 4(x2 – 2x – 15)
This can be factored further
a. Is it a difference of squares?
= 4(x – 5)(x + 3)
Find two numbers that multiply
to -15 and add to -2
b. Is it a perfect square trinomial?
1. Always look for a common factor first
2. Can it be factored further?
c. Are there two numbers which
multiply to c and add to b?