Factoring Cubic ExpressionsDate: 08/24/2010 at 18:25:50 From: katy Subject: factoring I don't know how to factor numbers with variables to the third power. For example, how do I factor this? 16x^3 - 250 Date: 08/25/2010 at 10:28:34 From: Doctor Ian Subject: Re: factoring Hi Katy, The first thing I'd do is look for other cubes. For example, I can write your cubic expression this way: 2(8x^3 - 125) = 2(2^3 x^3 - 5^3) = 2((2x)^3 - 5^3) What might you try next? Now, if you're not particularly facile with cubes, you could make things a little more visible by finding prime factors, and expanding exponents. For example, 16x^3 - 250 = 2*2*2*2*x*x*x - 2*5*5*5 |___| |___| |___| |_____|_________|______ Here are the cubes! In some ways, prime factors are a kind of x-ray machine for uncovering hidden structure in expressions. :^D Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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