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Divide using polynomial long division(Algebra 2)

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2 Answers

 

                            5x2  +  17x  +31

         x -3x + 4 /----------------------------------------------------

                          5x4     +2x3   +0x2    -9x    +12

                          5x4    -15x+20x2

                                   17x3   -20x2

                                   17x3  -51x2  +68x  

                                            31x2   -77x

                                            31x2  -93x  +124

                                                      16x - 112

So the polynomial and modulus:

5x2 +17x +31 + (16x - 112)/(x2 -3x +4)                                                                                  

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                                       5x2 + 17x + 31

x2 - 3x + 4  |  5x4 + 2x3 +  0x2  -  9x +  12

                    5x4 - 15x3 + 20x2

                            17x3 - 20x2  -  9x

                            17x3 - 51x2 + 68x

                                     31x2  -  77x +  12

                                     31x2  -  93x + 124

                                                16x  -  112

 

Thus 5x4 + 2x3 - 9x + 12 = (5x2 + 17x + 31)(x2 - 3x + 4) + 16x - 112