Download x – 3 = 0

Factoring
Trinomials
(x + 5)(x + 4)
2
x
+ 9x + 20
5+4
5x4
Factor
2
x + 9x + 20
Factoring is doing the
opposite of FOIL
2
x
+ 9x + 20
(x +4)( x +5 )
We know
we want to
end up with
2 binomials
Find 2 numbers with a product of 20
1 x 20
2 x 10
4x5
That can be combined by addition to equal 9
Check with FOIL
( x + 4)(x + 5)
2
x + 5x + 4x + 20
2
x + 9x + 20
2
x
+ 8x + 16
(x +4)(x +4)
We know
we want to
end up with
2 binomials
Find 2 numbers with a product of 16
1 x 16
2x8
4x4
That can be combined by addition to equal 8
Check with FOIL
( x + 4)(x + 4)
2
x + 4x + 4x + 16
2
x + 8x + 16
+ 2x +- 3
( x - 1)( x + 3)
2
x
We know
we want to
end up with
2 binomials
The – means that one sign will be negative and
one will be positive
Find 2 numbers with a product of 3
1x3
That can be combined by addition to equal +2
Check with FOIL
( x - 1)(x + 3)
2
x + 3x + -x + -3
2
x + 2x - 3
+ x+
-12
( x - 3)( x + 4)
2
x
We know
we want to
end up with
2 binomials
The – means that one sign will be negative and
one will be positive
Find 2 numbers with a product of 12
1 x 12
2x6
3x4
That can be combined by addition to equal +1
Check with FOIL
( x - 3)(x + 4)
2
x + 4x+ -3x+ -12
2
x + x - 12
+- 2x +- 8
( x - 4)( x + 2)
2
x
We know
we want to
end up with
2 binomials
The – means that one sign will be negative and
one will be positive
Find 2 numbers with a product of 8
1x8
2x4
That can be combined by addition to equal -2
Check with FOIL
( x - 4)(x + 2)
2
x + 2x+ -4x + -8
2
x - 2x - 8
- 6x + 9
+
( x - 3)( x - 3)
2
x
We know
we want to
end up with
2 binomials
The +9 and -6 means that both signs will be
negative
Find 2 numbers with a product of 9
1x9
3x3
That can be combined by addition to equal -6
Check with FOIL
( x - 3)(x - 3)
2
x + -3x+ -3x + 9
2
x - 6x + 9
+- 7x + 10
( x - 2)( x - 5)
2
x
We know
we want to
end up with
2 binomials
The +10 and -7 means that both signs will be
negative
Find 2 numbers with a product of 10
1 x 10
2x5
That can be combined by addition to equal -7
Check with FOIL
( x - 2)(x - 5)
2
x + -5x+ -2x + 10
2
x - 7x + 10