Factoring an Equation
Date: 3/11/96 at 19:43:58 From: Anonymous Subject: Algebra/factoring My math problem is if you have the equation x2 (x squared) * (times) 2x + 3 = 0 how do you factor it? I have tried many ways and I have gotten completely lost so if you could start at the beginning I would really appreciate it. The teacher says that it will come out to be some answer without decimals. Thank You, Melissa Lott
Date: 3/12/96 at 10:3:56 From: Dr. Elise Subject: Re: Algebra/factoring Hi Melissa, I see your dilemma. The problem you have stated is: x^2 * 2x + 3 = 0 Which is really: 2x^3 + 3 = 0 2x^3 = -3 x^3 = -3/2 I'm sure even your teacher will agree that this is not going to turn out as "some answer without decimals". The last time I checked, the cube root of negative three- halves was an imaginary decimal. No wonder you're completely lost! My best guess is that something went wrong when you copied the problem - I'd advise you to check it out. I'll show you what I'll bet the problem was, though! Okay. Factoring. Let's say that the "times" should really have been a "plus". x^2 + 2x + 3 = 0 Now we go through the usual factoring process. The coefficient of the x^2 term is 1, so we don't worry about it any more - both factors are going to look like (x plus or minus something). The 3 is a prime number, so the only way we're going to be able to factor it is 1 * 3. So we know our answer is going to look like either: (x + 1)(x + 3) or (x - 1)( x - 3) in order to come out with a positive x^2 and a positive 3. Does either of these combinations give us a positive 2x? Nope. So we know that this particular problem isn't factorable. Let's say the problem was: x^2 + 2x - 3 = 0 instead. We still end up with 1 * 3 for the 3, but it has to be either - 1 * 3 or 1 * -3 to get a negative 3. And we know we want a positive 2x, so we know that the bigger number, 3, has to be the positive one (otherwise we'd end up with a negative 2x). So we get (x - 1)(x + 3) = 0 This is the only way that I can see to factor anything close to what's in your problem into an answer with whole numbers. Does this help? Even if the problem was: x^2 * (2x + 3) = 0 then we still end up with either x^2 = 0 or (2x + 3) = 0, and our solutions would be x = 0, x = 0, (twice, because it's x^2, so it has 2 factors) and x = - 3/2, which is a fraction. Good luck, and let me know how it turns out. - Dr. Elise The Math Forum
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