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Lesson Easy Trinomial +C (Pt2)
Contributed by: Pappal
When factoring easy trinomials
When factoring easy trinomials
x2 - 8x + 12
We use the last sign to know...
When factoring easy trinomials
x2 - 8x + 12
last sign
whether the factor signs are the same
We use the last sign to know...
When factoring easy trinomials
x2 - 8x + 12
last sign
whether the factor signs are the same
( x +   ) ( x +   )
( x -   ) ( x -   )
We use the last sign to know...
When factoring easy trinomials
x2 - 8x + 12
factor signs the same
last sign
whether the factor signs are the same
( x +   ) ( x +   )
( x -   ) ( x -   )
We use the last sign to know...
When factoring easy trinomials
x2 - 8x + 12
last sign
or different
whether the factor signs are the same
( x +   ) ( x +   )
( x -   ) ( x -   )
We use the last sign to know...
When factoring easy trinomials
x2 - 8x + 12
different signs
last sign
or different
( x -   ) ( x +   )
( x -   ) ( x +   )
?
x2 + 5x - 2
Match the trinomial with the correct factor signs
( x -   ) ( x -   )
?
x2 - 5x + 2
( x +   ) ( x +   )
?
x2 + 5x + 2
x2 - 6x + 8
When the last sign is positive
x2 - 6x + 8
positive sign
previous sign
then we use the previous sign to determine
When the last sign is positive
what are signs will be
x2 - 6x + 8
So we know the factor signs are
previous sign
then we use the previous sign to determine
When the last sign is positive
what are signs will be
x2 - 6x + 8
So we know the factor signs are
previous sign
then we use the previous sign to determine
When the last sign is positive
what are signs will be
( x -   ) ( x -   )
x2 - 6x + 8
( x -   ) ( x +   )
Match the factor signs with the correct trinomial
x2 - 2x - 1
?
( x +   ) ( x +   )
x2 + 2x + 5
?
( x -   ) ( x -   )
x2 - 2x + 5
?
The last sign also tells us...
x2 - 6x + 8
last sign
The last sign also tells us...
...whether we...
x2 - 6x + 8
last sign
The last sign also tells us...
...whether we...
...add or subtract...
x2 - 6x + 8
last sign
The last sign also tells us...
...whether we...
...add or subtract...
x2 - 6x + 8
...our factors.
last sign
The last sign also tells us...
...whether we...
...add or subtract...
Let's explain.
x2 - 6x + 8
...our factors.
last sign
First, list all the factors of 8...
x2 - 6x + 8
First, list all the factors of 8...
1 and 8
x2 - 6x + 8
First, list all the factors of 8...
What do you multiply 4 by to get 8?
1 and 8
2 and 4
x2 - 6x + 8
First, list all the factors of 8...
then we look at our last sign
1 and 8
2 and 4
x2 - 6x + 8
First, list all the factors of 8...
then we look at our last sign
1 and 8
2 and 4
x2 - 6x + 8
last sign
First, list all the factors of 8...
then we look at our last sign
since the last sign is a positive
1 and 8
2 and 4
x2 - 6x + 8
positive
we want to ADD those factors to get the middle number
First, list all the factors of 8...
then we look at our last sign
since the last sign is a positive
1 and 8
2 and 4
x2 - 6x + 8
positive
we want to ADD those factors to get the middle number
First, list all the factors of 8...
then we look at our last sign
since the last sign is a positive
the middle number is 6
1 and 8
2 and 4
x2 - 6x + 8
middle number
we want to ADD those factors to get the middle number
First, list all the factors of 8...
then we look at our last sign
since the last sign is a positive
the middle number is 6
1 and 8
2 and 4
x2 - 6x + 8
1 + 8 ≠ 6
middle number
we want to ADD those factors to get the middle number
First, list all the factors of 8...
then we look at our last sign
since the last sign is a positive
the middle number is 6
1 and 8
2 and 4
x2 - 6x + 8
1 + 8 ≠ 6
middle number
we want to ADD those factors to get the middle number
First, list all the factors of 8...
then we look at our last sign
since the last sign is a positive
the middle number is 6
1 and 8
2 and 4
x2 - 6x + 8
1 + 8 ≠ 6
2 + 4 = 6
middle number
we want to ADD those factors to get the middle number
First, list all the factors of 8...
then we look at our last sign
since the last sign is a positive
the middle number is 6
1 and 8
2 and 4
x2 - 6x + 8
1 + 8 ≠ 6
2 + 4 = 6
middle number
So 2 and 4 are my factors
1 and 8
2 and 4
x2 - 6x + 8
1 + 8 ≠ 6
2 + 4 = 6
and since I already know my factor signs
So 2 and 4 are my factors
1 and 8
2 and 4
x2 - 6x + 8
1 + 8 ≠ 6
2 + 4 = 6
and since I already know my factor signs
( x -    ) ( x -    )
So 2 and 4 are my factors
1 and 8
2 and 4
x2 - 6x + 8
1 + 8 ≠ 6
2 + 4 = 6
and since I already know my factor signs
( x -    ) ( x -    )
So 2 and 4 are my factors
1 and 8
2 and 4
x2 - 6x + 8
I just plug in my factors
1 + 8 ≠ 6
2 + 4 = 6
and since I already know my factor signs
( x - 2 ) ( x - 4 )
So 2 and 4 are my factors
1 and 8
2 and 4
x2 - 6x + 8
I just plug in my factors
1 + 8 ≠ 6
2 + 4 = 6
( x - 2 ) ( x - 4 )
x2 - 6x + 8
and that's the answer!
x2 + 8x + 12
The last sign is +
x2 + 8x + 12
The last sign is +
so my factor signs are
x2 + 8x + 12
the same
different
The last sign is +
The previous sign is +
so my factor signs are
x2 + 8x + 12
    the same
The last sign is +
The previous sign is +
so my factor signs are
x2 + 8x + 12
so my factor signs are both
    the same
positive
negative
So I know that my factors signs look like
( x +   ) ( x +   )
( x -   ) ( x -   )
( x -   ) ( x +   )
( x +   ) ( x -   )
x2 + 8x + 12
So I know that my factors signs look like
I know I must
    ( x +   ) ( x +   )
x2 + 8x + 12
add factors
subtract factors
So I know that my factors signs look like
I know I must
    ( x +   ) ( x +   )
x2 + 8x + 12
    add factors
to get 8
The factors of 12 are...
    ( x +   ) ( x +   )
x2 + 8x + 12
    1 and 12
    2 and 6
    3 and 4
The factors of 12 are...
    ( x +   ) ( x +   )
x2 + 8x + 12
    1 and 12
    2 and 6
    3 and 4
The factors of 12 are...
    ( x +   ) ( x +   )
x2 + 8x + 12
1 and 12
2 and 6
3 and 4
which one
adds to get
8?
So my factors are...
    ( x +   ) ( x +   )
x2 + 8x + 12
So my factors are...
    ( x +2 ) ( x +   )
x2 + 8x + 12
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