Factoring ax2 bx c (PowerPoint)

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					Factoring ax2 + bx + c, a = 1
                  April 1st, 2011
Recap
 You have all learned how to multiply binomials.
                ( x  4)(x  3)

 What pattern do you see?
 Most of the time, NOT ALWAYS, the product is a
  …
 Today you are going to learn how to factor
  trinomials, when a = ….
 Essentially we will be converting from … form to
  … form.
 On Monday we will factor trinomials where a≠1.
Patterns for Expanding & Factoring
 Expand the following and look for a pattern that
  would help you go backwards to factored form
  from the expanded form.
   ( x  7)(x  3)                           ...
   ( x  4)(x  5)                           ...
   ( x  6)(x  3)                           ...
    ( x  3)(x  3)                          ...
The two numbers in the brackets, when in factored form, … to give
 the … term and … to give the … term in the simplified trinomial.
Factoring a Trinomial, a = 1
 A trinomial is a polynomial with … terms in the
  form ax2 + bx + c, where a ≠ 0, b ≠ 0, & c ≠ 0.
 The pattern we discovered showed that to write
  in factored form, we are going to be looking for
  two integers that multiply to… and add to …
 These two numbers are what end up being …
  and … in factored form.
 Note: This pattern only works when a = …!!
 Tomorrow, we will learn a slightly different
  method for when a ≠ 1.
Factoring a Trinomial

 2 x  10x  12
   2               Always check for …
                    factor first!
                   If there are any, factor
                    them out.
                   We are looking for two
                    numbers that have a
                    product of … and a sum
                    of …
                   What are the numbers?
                    …&…
                   Check by expanding.
Examples
 Factor the following trinomials.


1)   x  5 x  14
      2
                              2)     x  10 x  25
                                      2




3)   x  5 xy  6 y
      2               2        4) 3 x 2 y  9 xy  54 y
Application
 The volume of a cube is given by the
  expression 3x  30x  72 cm3. Factor fully to
                 2

  find the expressions for the dimensions of the
  cube.

  3x 2  30x  72




  Therefore, …
Assigned Work



 P.240-241
# 1all, 2cd,3def,4ace,5def,6,7ace,8ad,9cd,10bc,
  11bc,

				
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