Lesson Easy Trinomial -C
When factoring an easy trinomial
easy trinomial
When factoring an easy trinomial
x2 +4x - 12
the most important sign  is the last sign
When factoring an easy trinomial
x2 +4x - 12
the most important sign  is the last sign
When factoring an easy trinomial
x2 +4x - 12
last sign
the most important sign  is the last sign
which tells you two things...
When factoring an easy trinomial
x2 +4x - 12
the most important sign  is the last sign
which tells you two things...

whether the signs are the same or different

When factoring an easy trinomial
x2 +4x - 12
the most important sign  is the last sign
which tells you two things...

whether the signs are the same or different

and whether to add of subtract factors
When factoring an easy trinomial
x2 +4x - 12
x2 - 4x + 7
Which sign is the most important sign?
+
?
x2 + 4x - 7
-
?
When the last sign is a negative...
x2 +4x - 12
When the last sign is a negative
When the last sign is a negative...
x2 +4x - 12
negative
then we know that our factor signs will be different
When the last sign is a negative
When the last sign is a negative...
x2 +4x - 12
negative
then we know that our factor signs will be different
When the last sign is a negative
When the last sign is a negative...
( x -    ) ( x +    )
x2 +4x - 12
negative
then we know that our factor signs will be different
When the last sign is a negative
When the last sign is a negative...
( x -    ) ( x +    )
x2 +4x - 12
negative
different
signs
( x -    ) ( x -    )
?
x2 - 3x + 4
Match the factor signs with the correct trinomial.
( x -    ) ( x +    )
?
x2 + 3x - 4
( x +    ) ( x +    )
?
x2 + 3x + 4

We also know that the factors of 12 will have to be

( x -    ) ( x +    )
x2 +4x - 12
negative

We also know that the factors of 12 will have to be

subtracted to get 4.
( x -    ) ( x +    )
x2 +4x - 12
negative

We also know that the factors of 12 will have to be

subtracted to get 4.
( x -    ) ( x +    )
x2 +4x - 12
1 and 12
negative

We also know that the factors of 12 will have to be

subtracted to get 4.
( x -    ) ( x +    )
x2 +4x - 12
1 and 12
negative
12 - 1 ≠ 4

We also know that the factors of 12 will have to be

subtracted to get 4.
( x -    ) ( x +    )
x2 +4x - 12
1 and 12
negative
12 - 1 ≠ 4
What do you multiply 6 by to get 12?

We also know that the factors of 12 will have to be

subtracted to get 4.
( x -    ) ( x +    )
x2 +4x - 12
1 and 12
2 and 6
negative
12 - 1 ≠ 4

We also know that the factors of 12 will have to be

subtracted to get 4.
( x -    ) ( x +    )
x2 +4x - 12
1 and 12
2 and 6
negative
12 - 1 ≠ 4

6 - 2 = 4

Solve

We also know that the factors of 12 will have to be

subtracted to get 4.
( x -    ) ( x +    )
So my factors are 2 and 6
x2 +4x - 12
1 and 12
2 and 6
negative
12 - 1 ≠ 4

6 - 2 = 4

Which factors are the correct ones for this problem?
1 and 30

2 and 15

3 and 10

4 and 6

x2 - 7x - 30
What are the correct factors?
( x -    ) ( x +    )
x2 +4x - 12
1 and 12
2 and 6
3 and 3
But where do I put the factors?
( x -    ) ( x +    )
x2 +4x - 12
2 and 6
Should the 2 be negative and the 6 be positive?
But where do I put the factors?
( x -    ) ( x +    )
x2 +4x - 12
2 and 6
Or should the 6 be negative and the 2 be positive?
Should the 2 be negative and the 6 be positive?
But where do I put the factors?
( x -    ) ( x +    )
x2 +4x - 12
2 and 6
previous sign
The way to tell is to look at the previous sign
( x -    ) ( x +    )
x2 +4x - 12
2 and 6
The way to tell is to look at the previous sign
the bigger factor
( x -    ) ( x +    )
x2 +4x - 12
2 and 6
6 is bigger than 2
The way to tell is to look at the previous sign
the bigger factor
has the same sign as the previous sign
( x -    ) ( x +    )
x2 +4x - 12
2 and 6
6 is bigger than 2
previous sign
Since the previous sign is positive
( x -    ) ( x +    )
x2 +4x - 12
2 and 6
previous sign
Since the previous sign is positive
the 6 gets the plus sign
( x -    ) ( x +    )
x2 +4x - 12
2 and 6
previous sign
Since the previous sign is positive
the 6 gets the plus sign
( x - 2 ) ( x + 6 )
x2 +4x - 12
2 and 6
Fill in the blank
and that's our answer!
( x - 2 ) ( x + 6 )
x2 +4x - 12
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