Time remaining:
Use synthetic division to complete the indicated factorization

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x^4-4x^3-5x^2+36x-36=(x-3) ()

Mar 22nd, 2015

Tricky to do the formatting here, but here goes:

         x^3     
        ________________________

x-3 ) x^4 - 4x^3 - 5x^2 + 36x - 36
        -x^4 +3x^3
                   -x^3 - 5x^2 + 36x - 36


Next term:

         x^3   -x^2
        ________________________

x-3 ) x^4 - 4x^3 - 5x^2 + 36x - 36
        -x^4 +3x^3
                   -x^3 - 5x^2 + 36x - 36
                   +x^3 - 3x^2
                            - 8x^2 + 36x - 36


Next term:

         x^3   -x^2  - 8x
        ________________________

x-3 ) x^4 - 4x^3 - 5x^2 + 36x - 36
        -x^4 +3x^3
                   -x^3 - 5x^2 + 36x - 36
                   +x^3 - 3x^2
                            - 8x^2 + 36x - 36
                            +8x^2 - 24x
                                           12x - 36


Next term:

         x^3   -x^2  - 8x + 12
        ________________________

x-3 ) x^4 - 4x^3 - 5x^2 + 36x - 36
        -x^4 +3x^3
                   -x^3 - 5x^2 + 36x - 36
                  +x^3 - 3x^2
                            - 8x^2 + 36x - 36
                            +8x^2 - 24x
                                           12x - 36
                                           -12x + 36
                                                      0

So the factorization (x-3)(?) = (x-3)(x^3 - x^2 - 8x + 12) 






Mar 21st, 2015

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