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Math Help - Solving Polynomial Functions With a Degree of 4

  1. #1
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    Exclamation Solving Polynomial Functions With a Degree of 4

    i am doing some exam prep for my functions class but i can't seem to remember how to solve equations with a degree of 4 or higher. Here is the example i am working on. Thank in advanced.

    2x^4 + 11x^3 + 9x^2 – 14x – 8 = 0
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  2. #2
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    Use synthetic division on suspected roots to confirm they are roots and reduce the power of the polynomial remainder.

    For this particular problem, a trick:

    When all of the coefficients of a polynomial sum to 0, then 1 is one of the roots. Confirm with division and then work on the third degree polynomial that remains.
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  3. #3
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    If you want to solve the long way, use this calculator here that shows the 4 real roots and how to get there:

    Solving Quartic Equations

    This shows how to break the quartic into a cubic and go from there if you decide not to take the synthetic division route.
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