PFMexample.py

class Example:

    def __init__(self):
        print("You have choosen to view an example. To advance each step press enter.\nIn the example we will use the polynomial: 2x^4 + x^3 - 19x^2 -9x +9\n\n")
        input("")
        print("First you will find the factors of the leading coefficient: q = +-1, +-2")
        input("")
        print("Then you will need the factors of the trailing constansep=' 't term: p = +-1, +-3, +-9")
        input("")
        print("You will then need to list the possible zeroes by taking p and dividing by q: +-1/1, +-1/2, +-3/1, +-3/2, +-9/1, +-9/2")
        print("These can be reduced to: +-1, +-1/2, +-3, +-3/2, +-9, +-9/2")
        input("")
        print("When you have the set of all possible zeroes from the polynomial you can then use synthetic division to test for each:\n")
        print("1 | 2  1 -19 -9    9\n  |    2   3 -16  -25\n  --------------------\n    2  3 -16 -25  -16\n\nThe remainder is not a 0 therefore 1 is not a root.")
        input("")
        print("-1 | 2  1 -19  -9    9\n   |   -2   1  18   -9\n   -------------------\n     2  -1 -18  9    0\n\nThe remainder is a 0 therefore -1 is a root.")
        input("")
        print("1/2 | 2  1 -19 -9    9\n    |    1   1 -9   -9\n    ------------------\n      2  2 -18 -18   0\n\nThe remainder is a 0 therefore 1/2 is a root.")
        input("")
        print("-1/2 | 2  1 -19   -9     9\n     |   -1   0   19/2  -1/4\n     ------------------------\n       2  0  -19  1/2   35/4\n\nThe remainder is not a 0 therefore -1/2 is not a root.")
        input("")
        print("3 | 2  1 -19   -9    9\n  |    6  21   6    -9\n  --------------------\n    2  7   2  -3     0\n\nThe remainder is a 0 therefore 3 is a root.")
        input("")
        print("-3 | 2  1   -19   -9    9\n   |    -6   15   12    -9\n   ------------------------\n     2  -5   -4    3     0\n\nThe remainder is a 0 therefore -3 is a root.")
        input("")