Transcript Factoring Trinomials using common factors

Factoring Trinomials
using common factors

2x  4x  6x
2
2x (x  2x  3)
3
2


This sign tells
you to Subtract
The factors.
x
2
3
x 3
x 1
3x

2
Remember – always check
for GCF first!!
Factor out everything that
ALL terms have in common.
In this case, all numbers are
even so they have a 2 in
common, and each term has
at least 1 x.
Now, use the tic-tac-toe
method on the trinomial.
Don’t forget to check yourself,
multiply ACROSS (L to R) all rows
and UP all columns to see if you
get the correct products.
3x  2x
 1x
Now bring down your
GCF!!!
2x ( x  3) ( x  1)

3x  3x  18 x
2
3x (x  x  6)
3
2


This sign tells
you to Subtract
The factors.
x
2
6
6x

2
Remember – always check
for GCF first!!
Factor out everything that
ALL terms have in common.
In this case, all numbers
have a 3 in common, and
each term has at least 1 x.
Now, use the tic-tac-toe
method on the trinomial.
Don’t forget to check yourself,
multiply ACROSS (L to R) all rows
and UP all columns to see if you
get the correct products.
x  3 3x  1x
x  2 2 x
3x ( x  3)( x  2)
Now bring down your
GCF!!!
12 x y  24 x y  15x y
4
3
2
2
3
3 x y (4x  8xy  5 y )
2
2
2
Now, use the tic-tac-toe method on the
trinomial.
(1)(20) (2)(10)
(1)(4) or (2)(2) Which
one? Multiply across
the row for help!
4x
2
 5y
(4)(5) Which
one will subtract to
give +8?
2
2x
5y
2x
1 y
20x y
2
2
10x y
 8xy
2 x y
Factor out EVERYTHING that
ALL terms have in common.
The numbers have 3 in
common.
What is the smallest exponent
for “x”?
So, each term has 2x’s in
common.
What is the smallest exponent
on the “y”?
So each term has 1 y in
common.
Now divide out the number and
subtract the variables
exponents.
Now bring down your
GCF!!!
3 x y (2 x  5 y)(2 x  1y)
2
2 x y  2 x y  12 xy
3
2
2
3
4
2xy ( x  xy  6 y )
2
2
2
Factor out EVERYTHING that ALL terms
have in common.
Now divide out the number and subtract
the variables exponents
(1)(6) or
Now, use the tic-tac-toe method on the
trinomial.
(2)(3) ???
x
2
6 y 6x y
2
2
2
x 3y 3 x y   xy
x 2y 2 x y 2xy 2 ( x  3 y )( x  2 y)
Now bring down your
GCF!!!
What is different about this problem?
36 x  36 x  40
2
4 (9 x  9 x  10)
2
When the leading term is negative, just
factor out a negative number to make it
positive!!!.
(1)(90)
(2)(45)
(3)(30)
(5)(18)
(6)(15) yes
9x
2
10 90x
3x
2
6 x
3x
5
15x
2
Factor out EVERYTHING that ALL terms
have in common.
Now divide out the negative number!!
Now, use the tic-tac-toe method on the
trinomial.
 9x
Now bring down your
GCF!!!
4 (3x  2) (3x  5)
18 x  21x  60
When the leading term is negative, just
factor out a negative number to make it
positive!!!.
2
3 (6 x  7 x  20)
2
(1)(20)
(2)(10)
(4)(5) yes –
Look at last
column.
6x
2
Factor out EVERYTHING that ALL terms
have in common.
(1)(120)
(2)(60)
Now divide out the negative number!!
(3)(40)
(4)(30)
Now, use the tic-tac-toe method on the
(5)(24)
trinomial.
(6)(20)
(8)(15) Yes
20 120x
2x
4
8 x
3x
5
15 x
2
 7x
Now bring down your
GCF!!!
3 (3x  4) (2 x  5)