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function

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given that f(x)= 3-7x+5x^2-x^3, factorise the polynomial completely, hence state the set of values of x for which the function is equal or less than zero .

  • function - ,

    -1 ( x^3 - 5 x^2 + 7 x - 3)

    I can see right away that x = 1 makes this zero because 8-8 = 0
    divide polynomial by (x-1)
    ******_x^2_-_4x____+_3_______________
    x-1 / x^3 - 5 x^2 + 7 x - 3
    *******x^3 - 1 x^2
    *******---------------------
    ***********- 4 x^2 + 7 x -3
    ***********- 4 x^2 + 4 x
    ***********-----------------
    *******************+ 3 x - 3
    *******************+ 3 x - 3
    remainder =0
    so
    -1 (x-1)(x^2 - 4 x + 3)
    so
    -1 (x-1)(x-1)(x-3)
    zeros at 1, 1 (double,just hits axis) and 3
    graph it remembering the - sign

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