L1. The document provides information on different factoring techniques: L1.1 Common monomial factoring, difference of two squares, sum and difference of two cubes, and perfect square trinomials. L1.2 Steps are outlined for each technique with examples provided. L1.3 Key aspects of each technique are highlighted such as requiring the first and last term to be perfect squares for difference of two squares.

1. L1. FACTORING
L1.1. CommonMonomial Factor
L1.2. Difference ofTwoSquares
L1.4. Perfect Square Trinomial
L1.3.SumandDifferenceofTwoCubes
L1.5. General Trinomial

2. FACTORING

3. FACTORING
thereverse ofmultiplication.
 finding thefactors ofagiven
product.

4. COMMON
MONOMIAL
FACTOR

5. PRIMENUMBER
Awhole number,
greater than 1,
whose only
factors are 1 and
itself.
Examples
:
3=
5=
(3)(1)
(5)(1)
PRIME
FACTORS

6. Example1.
A. 3x + 6
Write the factors of 3x: (3)(1)(x)
Write the factors of 6: (3)(2)
The GCF of 3x and 6 is (3).
Add the remaining factors. (x + 2)
Factors:(3)(x + 2)
=
x=
2

7. Example2.
B. 4x2 + 4x
Write the factors of 4x2: (2)(2)(x)(x)
Write the factors of 4x : (2)(2)(x)
The GCF of 4x2 and 4x is (2)(2)(x) or 4x.
Add the remaining factors. (x + 1)
Factors:(4x)(x + 1)
= x
=
1

8. Example3.
B. 5x + 15
Write the factors of 5x: (5)(x)
Write the factors of 10 : (5)(3)
The GCF of 5x and 10 is 5.
Add the remaining factors. (x+3)
Factors: (5)(x + 3)
= x
=
3

10. DIFFERENCE OF TWO
SQUARES
F2 - L2 = (F + L)(F - L)
Note:
first and last term must be perfect square.
Exponent must be an even number.
The operation is subtraction.

11. Example
A. 4a2 - 49
F2 - L2 =(F+L)(F-L)
Getthesquarerootoffirstandlastterm.
F= 4a
2
=2a
L= 49 = 7
Factors:(2a + 7)(2a - 7)
Connectwithplus
andminussign

12. Example
B. 9x2 - 25y4
F2 - L2 =(F+L)(F-L)
Getthesquarerootoffirstandlastterm.
F= 9x
2
=3x
L= 25y4 = 5y2
Factors: (3x+ 5y2)(3x - 5y2)
Connectwithplus
andminussign

14. SUM AND DIFFERENCE OF
TWO CUBES
F3+ L3 = (F + L)(F2- FL+ L2)
F3- L3 = (F - L)(F2+ FL +L2)

15. IFSUM(STEPS)
1. What are the cube roots of the first
and last terms?
2. Write their sum as the first factor. (x
+ y)
3. For the second factor, get the
trinomial factor by:
a. Squaring the first term of the
first factor.
b. Subtracting the product of
the first and last term of
the first factor.
c. Squaring the last term of the
first factor.
4. Write step 2 and step 3 in factored
form. (F+L)(F2- FL+ L2)
GiVEN: a3 + 64
F=
3
a3= a
L=
3
64= 4
(a + 4)
a2 -4a + 16
(a + 4)(a2-4a+16)
STEP1
STEP2
STEP3
STEP4

16. IFDIFFERENCE(STEPS)
1. What are the cube roots of the first
and last terms?
2. Write their difference as the first
factor. (x - y)
3. For the second factor, get the
trinomial factor by:
a. Squaring the first term of the
first factor.
b. Adding the product of
the first and second term of
the first factor.
c. Squaring the last term of the
first factor.
4. Write step 2 and step 3 in factored
form. (F-L)(F2+ FL+ L2)
27 - d3
F=
3
27 =3
L=
3
d3= d
(3 - d)
9 +3d + d2
(3 - d)(9 + 3d +d2)
STEP1
STEP2
STEP3
STEP4

18. RULE
(F2+ 2FL + L2)=(F + L)
2
perfectsquare factored
trinomial form
(F2-2FL + L2)=(F − L)
2
Note:
First and last term must be perfect square.
Exponent must be an even number.
Twice the product of f and l is the middle term

19. (STEPS)
1. Get the square
roots of the first and
last terms.
2. List down the
square as sum/
difference of two
terms as the case may
be.
3. Checking (twice the
product of F and L must
be equal to M.)
x2 + 10x + 25
F= x2= x
L= 25= 5
(x+5)
2
(2)(x)(5)=10x
STEP
1
STEP
2
CHECKING

20. (STEPS)
1. Get the square roots
of the first and last
terms.
2. List down the
square as sum/
difference of two terms
as the case may be.
3. Checking (twice the
product of F and L must
be equal to M.)
16x2 + 72x +
81
F= 16x2= 4x
L= 81= 9
(4x+9)
2
(2)(4x)(9)=72x
STEP1
STEP2
CHECKING

21. (STEPS)
1. Get are the
square roots of the
first and last terms.
2. List down the
square as sum/
difference of two
terms as the case
may be.
3. Checking (twice
the product of F and
L must be equal to
c2 - 30c + 225
F= c2= c
L= 225= 15
(c − 15)
2
(2)(c)(-15)=-30c
STEP1
STEP2
CHECKING

23. a. x2 + 10x + 16
Factors: (x+ 2)(x+8)
1.Factorthefirstterm.
(x + )(x + )
2.Lookfortwonumberswhoseproductis16and
whosesumis10.
The numbers we need are 2
and 8

24. b. x2 - 9x + 18
Factors: (x-3)(x-6)
1.Factorthefirstterm.
(x )(x )
2.Lookfortwonumberswhoseproductis18and
whosesumis-9.
The numbers we need are -
3 and -6

26. a. 2x2 - x - 6
Solution:Multiplyaandc.
(2)(-6)=-12
Writethepossiblefactorsof-12,whosesumisthemiddleterm,-1.
(-4)(3)=-12 -4+3=-1
(x-4)(x+3)
Dividetheconstantbythevalueofa. (x-
4
2
) (x+
3
2
)
Simplify,ifpossible.
(x-2)(2x+3)
(x-2)(2x+3) FINALANSWER
Connectitwiththefactorsofx2
Thenmultiplytheremaining
denominatorwithvariable.

27. b. 10x2 + 13x + 4
Solution:Multiplyaandc. (10)(4)=40
Writethepossiblefactorsof40whosesumisthe
middleterm,13.(8)(5)=40 8+5=13
(x+8)(x+5)
Dividetheconstantbythevalueofa. (x+
8
10
) (x+
5
10
)
Simplify,ifpossible.(x+
4
5
)(x+
1
2
)
(5x+4)(2x+1)
FINALANSWER
Connectitwiththefactorsofx2
Thenmultiplytheremaining
denominatorwithvariable
(5x+4)(2x+1)