FACTORING NOTES
I.
GREATEST COMMON FACTOR (GCF)
 Factor out the largest number that goes into each term
 Factor out the smallest power (exponent)
2.) 3x2 + 6x3 – 18x4 = 3x2 ( 1 + 2x – 6x2)
1.) 8t + 16 = 8(t + 2)
II.
GROUPING ( 4 TERMS)= (binomial)(binomial)
 Group the first two terms together, pick out the GCF of those
 Group the second two terms pick out the GCF. What is inside the ( ) must be exactly the same.
 Write what is inside the parenthesis then what is on the outside of the parenthesis.
Answer will be two binomials
***If the first two terms have no common factor then rearrange the terms so they have a common factor.
***If the second and last sign are different you should try factoring out a negative.
1.) 3x2 + 5x – 24xy – 40y = [3x2 + 5x ] + [-24xy – 40y]
x (3x + 5) + -8y (3x+5) = (3x + 5)( x – 8y)
III.
TRINOMIALS ( 3 TERMS) = (binomial)(binomial)
 If the coefficient of the square term is 1. Then you find the two numbers that multiply together to get
the last term, but add together for the middle term, *** Answer will be two binomials.
 If the coefficient of the square term is not 1, then
Step 1: Find two numbers that multiply to get the first term.
Step 2: Find the two numbers that multiply to get the last term.
Step 3: The middle term is found by adding the inside and the outside products.
OUTSIDE + INSIDE = MIDDLE TERM
IV.
DIFFERENCE OF TWO SQUARES ( 2 TERMS) = (binomial)(binomial) x2 – y2 = (x+y)(x –y)
 Must be subtraction between two squares.
Step 1: You write each term as a square
Step 2: Drop the squares, this is you binomial now write the other with a plus.
You will have one binomial with a plus and the other with a minus.
*** Answer will be usually be two binomials
1.) x2 – 36 = x2 – 62 = (x + 6) ( x – 6)
V.
2.) 49m2 – 100p2 = 72m2 – 102p2 = (7m+10p)(7m – 10p)
SUM OR DIFFERENCE OF TWO CUBES ( 2 TERMS) = (binomial)(trinomial)
 Can be addition or subtraction
𝒙𝟑 − 𝒚𝟑 = (𝒙 − 𝒚)(𝒙𝟐 + 𝒙𝒚 + 𝒚𝟐 ) or
𝒙𝟑 + 𝒚𝟑 = (𝒙 + 𝒚)(𝒙𝟐 − 𝒙𝒚 + 𝒚𝟐 )
Step 1: Write each term as a cube
Step 2: Drop cubes (this is your binomial).
Step 3: Do SOPPS for your trinomial Square first, Opposite sign, Product of what is in the
parenthesis, Plus +, Square last.
1.) a3 + 23 = (a + 2)(a2 – 2a + 4)
1
4
7
10
X
𝒙
2
5
8
11
3
6
9
12
2.) 64x3 – 125y3 = (4x)3 – (5y)3 =(4x – 5y) (16x2 + 20xy + 25y2)
1
16
49
100
X SQUARES
𝒙𝟐
4
9
25
36
64
81
121
144
1
64
343
1000
X CUBES
𝒙𝟑
8
125
512
1331
27
216
729
1728