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Math Help - How to factor 3*(x^4) + 4*(x^3) - 3

  1. #1
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    How to factor 3*(x^4) + 4*(x^3) - 3

    I know it has two x-intercepts but I'm not sure how to factor polynomials with degrees greater than 2..
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  2. #2
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    Re: How to factor 3*(x^4) + 4*(x^3) - 3

    It doesn't factor completely over the integers. You can factor it as x^3 (3x + 4) - 3 but that's about all you can do.
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    Re: How to factor 3*(x^4) + 4*(x^3) - 3

    There's no way I can find the exact values of the zeroes of this function algebraically?
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    Re: How to factor 3*(x^4) + 4*(x^3) - 3

    Both real roots are irrational. There is a quartic formula, but I wouldn't bother memorizing it. Newton's method is probably the best "algebraic" way of solving it.

    Let f(x) = 3x^4 + 4x^3 - 3. For some initial "guess" x_0, let x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} and, for i \ge 2, x_i = x_{i-1} - \frac{f(x_{i-1})}{f'(x_{i-1})}. As i gets larger, you should approach a root of f(x).
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