Factoring Cubic Polynomials
Date: 01/01/2002 at 00:22:38 From: Ash Subject: Factoring Cubic equations Hello Dr. Math, I was hoping that you could help me figure out a few problems on factoring. I know how to factor square polynomial equations, by using the quadratic formula. But I have a lot of problems factoring cubic polynomials. Would you be able to help me on a few of these problems? Thanks. 1) 10*x^3 - 3*x^2 - x = f(x) 2) 18*r^3 - 128*r^5*s^2 By the way, what does it mean to factor a polynomial into "linear factors"? Is that the same as regular factoring? Ash
Date: 01/01/2002 at 02:38:05 From: Doctor Paul Subject: Re: Factoring Cubic equations Factoring into linear factors means that each of the factors should be linear (i.e., of degree one). The first problem is a quadratic and you can apply the quadratic formula. Factor out an x from everything and then apply the quadratic formula to what's left behind. In the second problem, factor out the largest thing possible: 2*r^3 That gives: [2*r^3] * (9 - 64r^2*x^2) The second part is a difference of squares so it factors as well. Can you finish this? In general, factoring cubics is hard. The only way you can be expected to be able to factor cubics is if they are "special" cubics. By special, I mean cubics that are chosen in such a way that they factor nicely in ways with which you are already familiar. As a general rule for factoring cubics, try to factor out the largest thing possible and then see what's left behind. If you're lucky you can apply a readily available factoring technique to what's left behind and then you'll be finished with the problem. I hope this helps. Please write back if you'd like to talk about this some more. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/
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