INTEGRATED MATHEMATICS
FACTORING
FACTORING USING GCF
• Students will calculate the GCF
of 2 or 3 terms of a polynomial.
• Students will apply concepts of
GCFs and Factoring to write the
factored form of a polynomial.
FACTORING USING GCF
Steps
1. Find the greatest common
factor (GCF)
2. Divide the polynomial by the
GCF. The quotient is the other
factor.
3.Express the polynomial as the
product of the quotient and the
GCF.
FACTOR
𝑬𝒙. 𝟏)
𝟐
𝟔𝒙 + 𝟑𝒙
FACTOR
𝑬𝒙. 𝟐)
𝟒
𝟓𝒚 − 𝟐𝟎𝒚
𝟑
FACTOR
𝑬𝒙. 𝟑)
𝟐
𝟏𝟔𝒂 + 𝟐𝟎𝒂
FACTOR
𝑬𝒙. 𝟒)
𝟏𝟓𝒙 𝟓 − 𝟏𝟐𝒙 𝟒 + 𝟐𝟕𝒙 𝟑 − 𝟑𝒙 𝟐
FACTOR
𝑬𝒙. 𝟓)
− 𝟒𝒏 𝟑 − 𝟐𝒏 𝟐 − 𝟔𝒏
TRY THESE
𝟏)𝟒𝒙 𝟑 − 𝟐𝒙 𝟐
𝟐)𝟏𝟎𝒙 𝟓 − 𝟏𝟓𝒙 𝟐
𝟑)𝟏𝟖𝒙 𝟑 − 𝟐𝟕
𝟑
𝟐
𝟒)𝟒𝒙 − 𝟏𝟐𝒙 − 𝟏𝟖𝒙
𝟕
𝟓)𝟏𝟑𝒙𝒚 𝟑 − 𝟏𝟐𝒙 𝟐 𝒚 − 𝟏𝟖𝒙𝒚 𝟕
DIFFERENCE OF TWO SQUARES
Students will apply concepts of
Perfect Squares and Factoring to
write the factored form of the
Difference of Two Squares.
DIFFERENCE OF TWO SQUARES
 There must be two terms that
are both squares
 Examples of squares
There must be a minus sign
between the two terms
PERFECT SQUARES
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11²= 121
12² = 144
13² = 169
14² = 196
15² = 225
16² = 256
17² = 289
18² = 324
19² = 361
20² = 400
FACTORING DIFFERENCE OF T WO SQUARES
FORMULA
2
A
–
2
B
= (A + B)(A – B)
FACTOR
Ex. 6)
x 4
2
FACTOR
Ex. 7)
4 x  25
2
FACTOR
Ex. 8)
m  16n
6
2
FACTOR
Ex. 9)
36 x  25 y
2
2
FACTOR
Ex. 10)
1 x
2
FACTOR
Ex. 11)
169 y  81z
2
2
TRY THESE
𝟏) 𝒙 𝟐 − 𝟗
𝟐)𝟏𝟎𝟎𝒙 𝟐 − 𝟏𝟔
𝟑)𝟑𝟔𝒙 𝟒 − 𝟏𝟐𝟏
𝟒)𝟒𝒙 𝟐 − 𝒚 𝟐
𝟓)𝟐𝟓𝒂 𝟐 − 𝟒𝟗𝒃 𝟐
FACTORING COMPLETELY
Students will apply concepts of
GCFs, Perfect Squares, and
Factoring to write the factored
form of the Difference of Two
Squares.
FACTORING COMPLETELY
Means to factor until factoring is
no longer possible
FACTOR.
LOOK FOR GCF FIRST!
Ex. 12)
5  20 y
6
FACTOR.
LOOK FOR GCF FIRST!
Ex. 13)
a b  4ab
3
3
FACTOR.
LOOK FOR GCF FIRST!
Ex. 14)
18a b  50a
2 2
6
FACTOR.
Ex. 15)
12m  3n
4
8
FACTOR.
Ex. 16)
50 x  2
4
TRY THESE
𝟏) 𝟐𝟕𝒙 𝟐 − 𝟏𝟐
𝟐)𝟓𝟎𝒙 𝟐 − 𝟖
𝟑)𝟏𝟖𝒙 𝟒 − 𝟕𝟐
𝟒)𝟐𝟎𝒙 𝟐 − 𝟒𝟓𝒚 𝟐
𝟓)𝟕𝟓𝒂 𝟐 𝒃 − 𝟐𝟕𝒃 𝟑
FACTORING TRINOMIALS
FACTORING A TRINOMIAL:
2
𝑥 + 𝐵𝑥 + 𝐶
Students will apply concepts
of factoring to write the
factored form of a trinomial.
FACTORING A TRINOMIAL:
2
𝑥 + 𝐵𝑥 + 𝐶
1. Write two sets of
parenthesis,
(
)(
). These will be the
factors of the trinomial.
2. Think of factors of c that add
up to b.
FACTOR
Example 1
x  5x  6
2
FACTOR
Example 2
13  14m  m
2
FACTOR
Example 3
x  8 x  15
2
FACTOR
Example 4
x  9 x  20
2
FACTOR
Example 5
x  8 x  20
2
FACTOR
Example 6
x  4 x  12
2
RULES SUMMARY
If C is positive (+), use the sign of B
twice.
If C is negative (-), use a + and a -. Bigger
number is the sign of B.
TRY THESE
𝟏) 𝒙 𝟐 + 𝟖𝒙 + 𝟏𝟐
𝟐) 𝒙 𝟐 − 𝟓𝒙 + 𝟔
𝟑) 𝒛 𝟐 + 𝟏𝟐𝒛 − 𝟐𝟖
𝟒) 𝒙 𝟐 − 𝟗𝒙 − 𝟐𝟐
𝟓) 𝒂 𝟐 + 𝟐𝒂 + 𝟏