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Notes 8.5 – FACTORING x2 + bx + c
The first reason we need to an expression is to
represented an expression in a
simpler form.
The second reason is it allows us to equations.
FACTOR
EQUIVALENT
I. Why Factor?
SOLVE
Find the missing value in each equation.
1.) 2.) 2 7 12 4x x x x 2 9 14 2x x x x
3 7
The trinomial written as a product of two
binomials is in FACTORED FORM.
2x bx c
Our goal is to find two integers whose SUM is b and
PRODUCT is c.
Example: What is the factored form of 2 7 10?x x
2 7 10 2 5x x x x
II. When b > 0 and c > 0
1 & 10
Factors of
10
Sum of
Factors
2 & 5
11
7
Hint: Make a table!
Now find b.
Example: What is the factored form of 2 11 24?x x
2 11 24 3 8x x x x
1 & 24
Factors 24 Sum 11
2 & 12
11
25
3 & 8
4 & 6
14
10
Example: What is the factored form of 2 8 12?x x
2 8 12 2 8x x x x
III. When b < 0 and c > 0.
1 & 12
Factors 12 Sum 8
2 & 6
13
8
Hint: Since b is negative and c is positive, both factors must be negative!
Example: What is the factored form of 2 9 18?x x
2 9 18 3 6x x x x
2 & 9 Factors 18 Sum 9
3 & 6 119
Example: What is the factored form of 2 3 10?x x
2 3 10 2 5x x x x
IV. When c < 0.
1 & 10
Factors 10 Sum 3
2 & 5
9
3
Hint: Since c is negative, one factor is positive and the other negative!
2 & 5 3
Example: What is the factored form of 2 7 8?x x
2 7 8 1 7x x x x
2 & 4 Factors 8 Sum 7
1 & 827
71 & 8
Helpful Hints
If is close to or greater than , then the factors are
usually spread apart. Ex.
If is close to 1, then the factors are usually close together.
Ex.
b1
2c
2 8 20 2 10x x x x
b
2 20 5 4x x x x
Example: What is the factored form of 2 2?x x
2 2 is x x PRIME
1 & 2 Factors 2 Sum 1
1 & 2
33
V. Prime Trinomials
Since none of the factors have a sum of -1, the expression in PRIME
A rectangular lot has an area of What are the
possible dimensions of the lot?
VI. Applications2 6 16.x x
A lw
2 6 16x x x x 4 & 4
Factors 16 Sum 6
2 & 80
6
2 6 16 2 8x x x x
Homework :
Tonight: Section 8.5 pages 536-537 #’s 10-36 all
