Simple Trinomials of the
Form x2+bx+c Using Algebra
Tiles and Patterning
Key Points
l  Factoring
¡ The process of rewriting an expression as a product or
multiplication (i.e.) putting the brackets back.
l  Trinomials
¡ Polynomials with three terms. The first term is called the
quadratic term because it has a coefficient and a variable
with an exponent of 2, the second term is called the linear
term because it has a coefficient and a variable and the
third term is called the constant term because it is a
number.
l  Simple Trinomials
¡ Trinomials that have a quadratic term with a coefficient of 1.
Factoring x2+bx+c Using Algebra Tiles
l  Represent the expression x2+4x+3 with algebra tiles. (Start
with x2-tile and the 3- unit tiles. Then place the 4-x tiles.)
l  What are the length and width of the rectangle?
The length is x+3 and the width is x+1
Note: There are no other ways
to make rectangles with this set
of tiles.
Factoring x2+bx+c Using Algebra Tiles
(continued)
l 
l 
l 
l 
The dimensions of the rectangle are (x+1) and (x+3). These
are called the factors.
The expression x2+4x+3 can be rewritten as (x+1)(x+3).
You just factored a trinomial! Let s try another one!
Example:
1. 
Factor x2+5x+6 = (x+2)(x+3)
Is this the
only
possibility?
Which would
result in 5-x
tiles?
Factoring x2+bx+c Using Algebra Tiles
(continued)
l  Examples:
1.  Factor.
a)  x2+4x-12
= (x-2)(x+6)
b) x2-7x+10
c) x2-6x-7
= (x-2)(x-5)
= (x+1)(x-7)
Factoring x2+bx+c Using Patterning
l  To factor x2+bx+c follow these steps:
1.  Start the answer with an equal sign.
2.  Write two sets of brackets and inside each
bracket put the variable.
3.  Now examine the trinomial and find the two
numbers (we ll call them r and s) that are the
product of c and whose sum is b.
4.  Write these numbers with their signs in the
brackets.
l  Let s practice finding these two magic numbers
by completing the chart on the next slide!
r
s
r+s
rxs
4
3
7
12
3
-2
1
-6
6
8
14
48
-4
-2
-6
8
4
5
9
20
5
-2
3
-10
-3
1
-2
-3
-3
-7
-10
21
7
-2
5
-14
6
5
11
30
6
-9
-3
-54
14
-3
11
-42
-6
-9
-15
54
Factoring x2+bx+c Using Patterning
(continued)
l 
Did you notice?
¡  If c is positive and b is positive, then the factors will both
be positive. If c is positive and b is negative, then both will
be negative. If c is negative, the factors will have opposite
signs.
l 
l 
You re ready to factor some trinomials!
PRODUCT
You are looking for two
Example:
SUM
1. 
Factor x2+14x+45
= (x+9)(x+5)
The magic numbers
are +9 and +5.
numbers that multiply
together to give 45 and the
same two numbers must add
together to give 14.
Factoring x2+bx+c Using Patterning
(continued)
l 
Examples:
1. 
Factor each of the following:
a)  x2-2x-35
=(x-7)(x+5)
c)  x2-12x+20
=(x-10)(x-2)
e)  x2+3x-28
=(x+7)(x-4)
g)  x2-4x+4
=(x-2)(x-2)
i)  x2+6x-40
=(x+10)(x-4)
b) x2-15x+56
=(x-8)(x-7)
d) x2+3x+2
=(x+1)(x+2)
f) x2-x-30
=(x-6)(x+5)
h) x2+10x+16
=(x+8)(x+2)
j) x2+9x-22
=(x+11)(x-2)
Factoring Special Trinomials
l 
l 
Difference of Squares
¡  In the form, x2 - a2. They have no linear term, it can
therefore be written as 0x. In order to get a sum of 0,
the factors will have to be the same number with opposite
signs.
¡  To find the magic numbers, take the square root of the
number on the end.
Example:
1. 
Factor x2-36
=(x+6)(x-6)
Take the square root of 36. It is 6.
The magic numbers are +6 and –6.
Factoring Special Trinomials (continued)
l 
Examples:
1. 
Factor each of the following.
a)  x2-100
b) x2-49
=(x-10)(x+10)
=(x-7)(x+7)
c)  x2-16
=(x-4)(x+4)
d) x2-1
=(x-1)(x+1)
e)  x2-81
=(x-9)(x+9)
f) x2-121
=(x-11)(x+11)
Homework
l  Worksheet