Factor Out The Gcf Chart
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1Factor Completely
Factor Out The GCF
Answers will look like distributive problems
3
− 9x
2
27x
2
− 25x
+ 15x
y −18 y
3
2
10x
4x
= 9x
(3x −1)
2
= 5x(2x
− 5x + 3)
= 2y(2x
− 9)
2
2
Second Degree Trinomals
Second Degree Trinomals
Second Degree
2
± Bx + C
2
Binomials
± Bx + C
Ax
Ax
with A = 1
Perfect Squares
with A > 1
Trinomials with
Trinomials with a
The Difference of Two
POSITIVE LAST term
POSITIVE LAST term
Perfect Squares
2
± Bx + C with A > 1
Ax
2
± Bx + C
1x
− b
2
2
a
= (first x
± last
± last
) (first x
)
= (x ± last
) (x ± last
)
1
1
2
2
= (a + b)(a − b)
1
2
2
the 2 FIRST terms MULTIPLY to Ax
the 2 last terms MULTIPLY to C
the 2 LAST terms MULTIPLY to C
the 2 last terms ADD to B
2
− 49
4x
and the outer and inner products
7⋅ 2
= (2x + 7)(2x − 7)
14 ⋅1
ADD to Bx
2
− 15x + 14
x
2
2
− 25
36x
y
( )
2 • 3
⋅5
2
the 2 last terms multiply to 14
= (6xy + 5)(6xy − 5)
( )
•1
10 ⋅1
6
the 2 last terms add to −15
2
− 17x + 10
= (x − 14)(x − 1)
6x
The Sum of Two
the 2 FIRST terms multiply to 6
Perfect Squares
the 2 LAST terms multiply to 10
Trinomials with a
Does Not Factor
NEGITIVE LAST term
2
+ 4
= (6x − 5)(1x − 2)
x
2
± Bx − C
1x
does not factor
= (x ± last
) (x ± last
)
1
2
the outer product is − 12x
the 2 last terms MULTIPLY to C
2
the inner product is − 5x
+ 25
4x
the 2 last terms SUBTRACT to B
Prime
2 • 5
1•10
Trinomials with A >1
2
+ 1
16x
− 3x − 10
2
x
and a NEGITIVE LAST term
DNF
the 2 last terms multiply to −10
are factored like the ones above
the 2 last terms subtract to − 3
but the outer and inner products
= (x + 2)(x − 5)
SUBTRACT to Bx
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