Factoring Butterfly Method by 5VBfbV

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									Name:_________________Date:__________ 1
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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