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Math Help - Zeros and end behaviour polynomial curve

  1. #1
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    Zeros and end behaviour polynomial curve

    Okay, so it's exam review time... long story short, I remember a couple of methods of finding the zeros of a polynomial function. One is by using my calculator :P if it's cubic or quadratic.

    The other was to use the synthetic division, and another: long division.

    I have a feeling I'm missing something here. Could you guys help me out. The review question is:

    States the zeros and end behaviour of the following function:

    f(x)= 2x^3 + 3x^2 - x + 2
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  2. #2
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    Quote Originally Posted by mike_302 View Post
    Okay, so it's exam review time... long story short, I remember a couple of methods of finding the zeros of a polynomial function. One is by using my calculator :P if it's cubic or quadratic.

    The other was to use the synthetic division, and another: long division.

    I have a feeling I'm missing something here. Could you guys help me out. The review question is:

    States the zeros and end behaviour of the following function:

    f(x)= 2x^3 + 3x^2 - x + 2
    I'm afraid there isn't really any special hints and tips apart from trying out a few values until you get a zero!

    For example, you get a zero for x = -2. Which means that x+2 is a factor.

    Use long division, or indeed synthetic division, to divide 2x^2+3x^2-x+2 by (x+2), and the result will be a quadratic of the form ax^2+bx+c

    Then simply write the function as f(x) = (x+2)(ax^2+bx+c) = 0 ... and then use normal quadratic methods to factorise the quadratic and find the other two roots! (or use the quadratic formula).
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