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Lesson Easy Trinomials +C (Pt1)
Contributed by: Pappal
There are 5 steps to factor a polynomial
There are 5 steps to factor a polynomial
Look for GCF
There are 5 steps to factor a polynomial
Look for GCF
Look for a pattern
There are 5 steps to factor a polynomial
Look for GCF
Look for a pattern
Factor an easy trinomial
There are 5 steps to factor a polynomial
Look for GCF
Look for a pattern
Factor an easy trinomial
Factor a hard trinomial
There are 5 steps to factor a polynomial
Look for GCF
Look for a pattern
Factor an easy trinomial
Factor a hard trinomial
Grouping
We are going
to talk about
the third step
There are 5 steps to factor a polynomial
Look for GCF
Look for a pattern
Factor an easy trinomial
Factor a hard trinomial
Grouping
Factoring easy trinomials is  fairly simple.
a trinomial
Factoring easy trinomials is  fairly simple.
x2 - 4 x + 3
Factoring easy trinomials is  fairly simple.
The most important part is...
x2 - 4 x + 3
Factoring easy trinomials is  fairly simple.
The most important part is...
...the last sign.
x2 - 4 x + 3
last sign
What is the most part of these trinomials?
x2 - 10x - 20
-
?
x2 - 4x + 3
+
?
Identify the most important sign in these trinomials
x2 + 3x - 5
Identify the most important sign in these trinomials
x2 + 3x - 5
-
x2 - 4x + 2
Identify the most important sign in these trinomials
x2 - 4x -12
x2 + 3x - 5
-
x2 - 4x + 2
+
Identify the most important sign in these trinomials
x2 - 4x -12
x2 + 3x - 5
-
-
x2 + 8x + 4
x2 - 4x + 2
+
What is the most important sign in this trinomial?
x2 +5x -6
+
-
This sign tells you two things...
x2 - 4 x + 3
last sign
This sign tells you two things...
...the signs of your factors,
x2 - 4 x + 3
last sign
This sign tells you two things...
and whether you add or subtract the factors
...the signs of your factors,
x2 - 4 x + 3
last sign
For example...
For example...
x2 - 8x + 12
This polynomial has a  '+' for its last sign
For example...
x2 - 8x + 12
a plus sign
This polynomial has a  '+' for its last sign
so that means two things...
For example...
x2 - 8x + 12
This polynomial has a  '+' for its last sign
so that means two things...
1. the factor signs are the same
For example...
x2 - 8x + 12
This polynomial has a  '+' for its last sign
so that means two things...
2. the factors must be added
1. the factor signs are the same
For example...
x2 - 8x + 12
x2 - 3x - 12
factor signs are the same
factor signs are different
Answer each of the following
If the factors must be added then the sign must be...
x2 - 3x - 12
    factor signs are different
Answer each of the following
x2 + 8x + 3
this sign is plus
x2 - 8x + 12
this sign is plus
so that means...
x2 - 8x + 12
this sign is plus
so that means...
the factor signs will be the same
x2 - 8x + 12
so the factors will either look like this
this sign is plus
so that means...
the factor signs will be the same
x2 - 8x + 12
so the factors will either look like this
this sign is plus
so that means...
the factor signs will be the same
x2 - 8x + 12
( x +   ) ( x +   )
so the factors will either look like this
this sign is plus
so that means...
the factor signs will be the same
or this
x2 - 8x + 12
( x +   ) ( x +   )
( x -   ) ( x -   )
Match the factor signs with the correct trinomial
( x -   ) ( x -   )
?
x2 - 5x + 2
( x +   ) ( x -   )
?
x2 + 5x - 2
How do we tell which one it is?
x2 - 8x + 12

the double positive?

How do we tell which one it is?
x2 - 8x + 12

the double positive?

( x +   ) ( x +   )

How do we tell which one it is?
x2 - 8x + 12

the double positive

( x +   ) ( x +   )

How do we tell which one it is?
x2 - 8x + 12
or the double negative?

the double positive

( x +   ) ( x +   )

How do we tell which one it is?
x2 - 8x + 12
or the double negative
( x -   ) ( x -   )
previous
sign

the double positive

( x +   ) ( x +   )

How do we tell which one it is?
We can tell by the previous sign
x2 - 8x + 12
or the double negative
( x -   ) ( x -   )
if that sign is positive

the double positive

( x +   ) ( x +   )

How do we tell which one it is?
We can tell by the previous sign
x2 - 8x + 12
or the double negative
( x -   ) ( x -   )
then we use the double positive
if that sign is positive

the double positive

( x +   ) ( x +   )

How do we tell which one it is?
We can tell by the previous sign
x2 - 8x + 12
or the double negative
( x -   ) ( x -   )
then we use the double positive
if that sign is positive

the double positive

( x +   ) ( x +   )

How do we tell which one it is?
We can tell by the previous sign
x2 - 8x + 12
or the double negative
but if that sign is negative
( x -   ) ( x -   )
then we use the double positive
if that sign is positive

the double positive

( x +   ) ( x +   )

How do we tell which one it is?
We can tell by the previous sign
x2 - 8x + 12
or the double negative
but if that sign is negative
( x -   ) ( x -   )
double negative
then use the
( x -   ) ( x -   )
?
Match the factor signs with the correct trinomial
x2 - 4x + 5
( x +   ) ( x +   )
?
x2 + 4x + 5

( x -   ) ( x +   )

?
x2 - 4x - 5

( x +   ) ( x +   )

So since the previous sign is negative
negative
x2 - 8x + 12
( x -   ) ( x -   )

( x +   ) ( x +   )

then we use the double negative factors
So since the previous sign is negative
negative
x2 - 8x + 12
( x -   ) ( x -   )
Find the correct signs for the factor
(x -     )(x +     )
(x -   )(x -    )
(x +     )(x +     )
(x +    )(x -    )
x2 + 6x + 7
Find the correct signs for the factor
(x -     )(x +     )
(x -   )(x -    )
(x +     )(x +     )
(x +    )(x -    )
x2 - 6x + 7
Find the correct signs for the factor
(x -     )(x +     )
(x -   )(x -    )
(x +     )(x +     )
(x +    )(x -    )
x2 - 7x + 12
Find the correct signs for the factor
(x -     )(x +     )
(x -   )(x -    )
(x +     )(x +     )
(x +    )(x -    )
x2 + 7x + 12
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