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.
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
9.
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.
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
17.
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
22.
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