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Math Help - Help!! How to factorise x^3 - 9x^2 + 24x - 30?

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    Help!! How to factorise x^3 - 9x^2 + 24x - 30?

    Help! How to factorise x^3 - 9x^2 + 24x - 30?

    It seems according to the key, 2 roots are imaginary and 1 root is real.
    I need to know only the real one. Can someone please help!!!!!
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    Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?

    Can you find a factor of -30 that makes this expression equal 0?
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    Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?

    It doesn't factorise.
    A sketch graph shows that there is a single real root to the right of x = 4,
    and a table of values narrows it to between x = 5 and x = 6.
    You can get a better approximation if you wish, but you are then into your favourite numerical method.
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    Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?

    If you MUST try to get the exact real solution, I suggest you read this...
    Attached Files Attached Files
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    Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?

    Well if you have something in the form of ax^3+bx^2+cx+d=0 you can try doing synthetic division by x-1 and that will give you (x-1)q(x)+r=0.
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    Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?

    Quote Originally Posted by SMAD View Post
    Well if you have something in the form of ax^3+bx^2+cx+d=0 you can try doing synthetic division by x-1 and that will give you (x-1)q(x)+r=0.
    And this does what? I don't see where you are headed here.

    -Dan
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    Re: Help!! How to factorise x^3 - 9x^2 + 24x - 30?

    Hello, mathhawk!

    Help! .How to factorise: f(x) \:=\:x^3 - 9x^2 + 24x - 30\,?
    According to the key, 2 roots are imaginary and 1 root is real.

    It is not factorable.

    The only possible rational roots are: . \pm1,\:\pm2,\:\pm3,\:\pm5,\:\pm6,\:\pm10,\:\pm15, \:\pm30
    . . None of them are zeros of the polynomial.

    We find that: . \begin{Bmatrix}f(5) &=& \text{-}10 \\ f(6) &=& +6 \end{Bmatrix}

    Hence, there is a root (irrational) on the interval (5,\,6).


    Another possibility: a typo in the problem.
    . . Could the constant term be -20 or -36?
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