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Q&A #849

Teachers' Lounge Discussion: Factoring the sum and difference of two cubes

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From: Roger <rbreen@fccj.edu>
To: Teacher2Teacher Public Discussion
Date: 2007120511:03:20
Subject: teaching the factoring sum or difference of cubes

	
                   Factor:          x^3 + 8

1)  There are two factors: one is a binomial, the other a trinomial.

                           ( ____   ____ )( ___    ___    ___ )

2)   The binomial is the cube root of the first term:    x
                     the cube root of the second term    2
                     separated by the same sign as the original

                            (  x  +  2  )(                     )  

3)   The first term of trinomial is the square of the first term in
the binomial   x^2
     The last term of the trinomial is the square of the second term
in the binomial    +4 [This term is always positive because any real
number squared is positive.]

                            (  x  +  2  )(  x^2           + 4 )

4)   The middle term of the trinomial is always the OPPOSITE of the
product of the two terms in the binomial   - (x)(2) =  -2x

5)                          (  x  +  2  )(  x^2  -2x  + 4  )

  

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