Algebra 1 Factoring Summary Sheet
1st Step
ALWAYS!!!!
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See if a common factor exists in each term, if so factor out the GCF
Ex: 4 x  12 x  40 factor out the GCF of 4….. 4( x
2
2
 3x  10) then continue with 2nd step
Ex: x  2 x  16 x  32 there is nothing common in all 4 terms so proceed with 2 nd step.
3
2
2nd Step: Depends on the number of terms.
 If two terms remain(a binomial quadratic) Try factoring by The difference of two squares
a 2  b2  (a  b)(a  b)
Ex:
x 2  64  ( x  8)( x  8)
Remember: we can not factor x2 + 64

Ex: 144 x 2  9 y 2  (12 x  3 y)(12 x  3 y)
There is “no such animal” as the “sum of 2 squares”
If three terms remain - a trinomial! You can use our “First times Third” method
?
+
=?
1. First Times Third: Example e 2  16e  48 Factors of 48e2 that add to get -16 (-12e and -4e)
Notice lead coeff is 1 so:  (e
)(e
)
 (e  12)(e  4)
Always check with FOIL
2.
First Times Third when lead coefficient is not = 1
Ex: 24 x  7 x  6
2
Factors of -144x2
(-16x & 9 x)
+ = -7x
Notice Lead coeff is 24x2: (24 x
)( x
) or (12 x
)(2 x
) or (8 x )(3 x ) or (6 x )(4 x
)
(8 x  3)(3x  2)
The only one that works to “get -16x and 9x” is (8 x )(3 x
)
Always check with FOIL

If 4 terms remain Factor by grouping (Usually group 1st and 2nd terms – but sometimes it is 1st and 3rd or 1st and 4th)
Ex: x  2 x  9 x  18
3
2
let’s group 1st and 2nd:
x3  2 x 2  9 x  18
 x 2 ( x  2)  9( x  2)
 ( x  2)( x 2  9) but notice x2-9 is diff. of 2 sq
 ( x  2)( x  3)( x  3)
3rd & final Step: you can always check using FOIL and/or the Dist. Prop.!! You should “get what you started
with”
Put in SIMPLE
flow chart!