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Math Help - Naming Polynomials

  1. #1
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    Naming Polynomials

    I need to name this polynomial. y=(x+4)(x+1)(x-3)

    Would it be a cubic polynomial because it's all multiplying, or would it be a linear?

    Please explain it to me..
    Thanks
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  2. #2
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    Re: Naming Polynomials

    Its a cubic because once you expand it out (try it!) you get x cubed as the term with the highest order.
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    Re: Naming Polynomials

    It's definitely cubic. It has exactly three roots.
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  4. #4
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    Re: Naming Polynomials

    Naming of polynomial in general is in accordance to the Order of the equation.
    Now, what is order ?
    Consider a polynomial in a single variable 'x'. Write the polynomial in its fully expanded form. Now search for the term that has the highest power on 'x' (like x squared or cubed etc.) Now that gives you the order of the polynomial. Now the naming is simple
    Order Name
    1 Linear
    2 Quadratic
    3 Cubic
    4 Bi-quadratic
    and so on...

    Hope that clears it !
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  5. #5
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    Re: Naming Polynomials

    Quote Originally Posted by pratique21 View Post
    Naming of polynomial in general is in accordance to the Order of the equation.
    Now, what is order ?
    Consider a polynomial in a single variable 'x'. Write the polynomial in its fully expanded form. Now search for the term that has the highest power on 'x' (like x squared or cubed etc.) Now that gives you the order of the polynomial. Now the naming is simple
    Order Name
    1 Linear
    2 Quadratic
    3 Cubic
    4 Bi-quadratic
    and so on...

    Hope that clears it !
    I've always called an Order 4 polynomial a "Quartic".
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  6. #6
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    Re: Naming Polynomials

    to clarify: a general 4-th degree polynomial in x (or use your favorite variable name) is called a quartic (in x). a bi-quadratic is a quadratic in x2, which is a special kind of quartic.

    to continue:

    5-th degree polynomials are quintics, 6-th degree are sextics, and 7-th degree are septics. if you are dealing with even higher-level polynomials, although "latin" names do exists, it is usually easier to refer to them as "k-th degree polynomials" (and easier to remember, too).
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