# Factoring Butterfly Method by 5VBfbV

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Notes on Factoring: Butterfly Method
Factors are     This method will work when
numbers or      factoring x 2  bx  c or
expressions     ax 2  bx  c
that are                 a ∙c x2
multiplied to
ax2                    ax 2
get another
number or       factor1 x             factor 2  x
expression.             bx
We are trying   Some examples
to find what
1) Factor x  7 x  10
2
binomial
factors         a = 1, b = -7 and c = 10
multiply to
equal the
polynomial.

The factors are the simplified
terms
Name:_________________Date:__________ 2
Notes on Factoring: Butterfly Method
2) Factor x 2  4 x  12
a = 1, b = 4, c = -12

The factors are
3) Factor   4 x 2  4 x  15
a = 4, b = -4 and c = -15

The factors are the simplified
terms
Name:_________________Date:__________ 3
Notes on Factoring: Butterfly Method
4) Factor 5x 2  26x  5
a = 5, b = -26, c = 5

The factors are
5) Factor   6x 2  9 x  15
Factor out 3 first 3(2 x  3x  5
2
)

The factors are the simplified
terms
Name:_________________Date:__________ 4
Notes on Factoring: Butterfly Method
Try: Factor 2 x 2  3x  5
a= ,b=      ,c=

The factors are ______________
5) Factor   3x 2  x  10

The factors are
________________
Name:_________________Date:__________ 5
Notes on Multiplying: FOIL and BOX Methods
Multiplying Binomials:
FOIL           Outer            Last
(2x + 3)(x – 6)
First
Inner
F         O          I        L
= 2x(x) + 2x(-6) + 3(x) + 3(-6)
= 2x2 -12x + 3x – 18
= 2x2 – 9x-18
Area Model
(4x2 + 5)(3x2 – 2)
4x2       +5
3x2   12x4     15x2
-2   -8x2     -10

=      12x4 + 15x2 – 8x2 – 10
=      12x4 + 7x2 - 10
Name:_________________Date:__________ 6
Notes on Mult Polynomials : Distributive Prop.
Multiplying (x + 3)(x2 +2x+ 4)
Have to distribute:
x(x2 +2x+ 4) + 3(x2 +2x+ 4)
= x  2 x  4 x  3x  6 x  8
3     2          2

x 3  5x 2  10 x  8
Area Method
Multiply (x + 4)(x2 + 2x – 3)
Create a box           x2     +2x     -3
x3    2x2   -3x
x
4x2   8x    -12
+4
= x3 + 6x2 + 5x – 12
Name:_________________Date:__________ 1
Notes on Multiplying: FOIL and BOX Methods
Name:_________________Date:__________ 1
Notes on Multiplying: FOIL and BOX Methods

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