Factoring Methods
Download
Report
Transcript Factoring Methods
Factoring Methods
Powerpoint created by Linnea Tucker
Factoring with
Algebra Tiles
Factor 2x2 + 5x + 3
•
Using algebra tiles, build a rectangle containing the tiles specified in this
problem (2 x2-tiles, 5 x-tiles and 3 1-tiles). Remember that the lines between
the tiles within your pattern must be completely vertical or horizontal across the
entire pattern. Here is one possible arrangement:
•
After the pattern is established, it can be seen that the top edge of the pattern
(the length) is composed of tiles with dimensions 2x + 3. The side edge of the
pattern (the width) is composed of tiles with dimensions x + 1.
Consequently, 2x2 + 5x + 3 = (2x + 3)(x + 1).
Factoring Trinomials
Step 1 (ALWAYS!)
Can you factor out a Greatest
Common Factor (GCF)?
Example:
GCF = x
2x3 -7x2 + 6x
So, factor it out:
x ( 2x2 – 7x + 6))
Multiply (x + 2)(x + 3)
• Use FOIL
x2 + 3x + 2x + 6
x2 + 5x + 6
Notice the
Multiples of 6
Must add to 5
Factor Cracker
Factor Cracker
Factor
a
2
c
a 2 b
7 x ++ 66
22xx – 7x
2 up the
Stepa1:=set
b =table
-7
c=6
c6
–b7
Factor Cracker
Factor 2 x2 – 7 x + 6
2
6
Factors of
“a” go here
Factors of
“c” go here
–7
Factor Cracker
Factor 2 x2 – 7 x + 6
2
6
2
6
1
1
Factors of 2:
2 and 1
–7
Factors of 6:
1 & 6; -1 & -6;
2 & 3; -2 & -3
(Use trial and error
for placement)
Factor Cracker
2
2
1
Factor 2 x2 – 7 x + 6
Multiply on
6
The
sum
of
the
the diagonal;
right column
products
go
6 6
must
equal
here
+
the “b” term.
1 2
–7
It’s important to select the proper
sign for the factors you use.
2+ bx+ c
x
a
If the “b” term is negative and the “c” term is
positive, the “b” term factors must both be
negative.
If the “b” and “c” terms are both negative, then
the “b” term factors must have opposite signs
such that the right hand column produces a sum
that agrees with the “c” term sign.
Factor Cracker
2
2
1
Factor 2 x2 – 7 x + 6
The
sum
ofisn’t
the
If the
sum
If that doesn’t
6
right
column
correct,
swap
work, try the
must
equal
factors
and of
try
-1
-1
other factors
-6 -6
“b”and
term.
+ the
the “a”
“c”
again.
terms.
-1
-6 -2
-12
=
–7
Factor Cracker
2
2
1
Factor 2 x2 – 7 x + 6
The
If
This
that
other
doesn’t
6
factorsswap
work,
combination
of 6
are 2 & 3;
factors.
works!!
-2
-3 -3
-2
+ -2 & -3
-3
-2 -4
-6
=
–7
Factor Cracker
Factor 2 x2 – 7 x + 6
The
Usefactors
FOIL toof
2
6
confirm
the that
the
polynomial
factors are
( 2 x -3 ) -3
correct!
are:
( 1 x -2 ) -4
( 2x-3 ) ( x-2 )
–7
You Try These Ones:
1) Factor
2
x + x - 30
2) Factor 3x2 + 10x +8
3) Factor
2
x – 3x -18
(x+6)(x-5)
(3x+4)(x+2)
(x+3)(x-6)
4) Factor 10x2 - 27x +18
(5x-6)(2x-3)
Box Method
Factor: 2 x2 – 7x + 6
The
quadratic
2
term goes
here
Sums of the
linear term
go here
And here
The constant
term goes
here
2x
6
BoxaMethod
b
c
Factor: 2 x2 – 7x + 6
2x2
Sums of the
linear term
go here
-4x
6
And here
-3x
How do you
determine the
two linear terms?
Step 1: multiply
a·c
2·6 = 12
Step 2: find
factors of a·c that
sum to b.
-3 and -4
Box Method
Factor: 2 x2 – 7x + 6
To the left, list
2x
-3
3
x
2x2
-3x
-2
2
-4x
6
the GCF for each
row.
On the top, list
the GCF for each
column.
Each term takes
on the sign of the
box closest to it.
Box Method
Factor: 2 x2 – 7x + 6
2x
-3
3
x
2x2
-3x
-2
2
-4x
6
The
Factors
are:
(x-2)(2x-3)
Use FOIL to check your answer!!
You Try These Ones:
1) Factor
2
x + x - 30
2) Factor 3x2 + 10x +8
3) Factor
2
x – 3x -18
(x+6)(x-5)
(3x+4)(x+2)
(x+3)(x-6)
4) Factor 10x2 - 27x +18
(5x-6)(2x-3)