How to Factor
Date: 7/25/96 at 13:33:39 From: Anonymous Subject: An Example and Explanation of How to Factor Here's the problem: I'm working on this summer review packet and I have totally forgotten how to factor. I need help with stuff like 8x^2+3x-5. If you could just give me an example, I could probably get the rest myself. Thanks!
Date: 7/28/96 at 20:33:0 From: Doctor Erich Subject: Re: An Example and Explanation of How to Factor Louie, There are a couple of ways to factor polynomials. If you look at a polynomial like 8x^2+3x-5, you can notice a couple of things which will help you factor it. First of all, the coefficient of the x^2 term and the coefficient of the constant(x^0) term, in this case 8 and -5 , are very helpful. It tells you that if the polynomial is factorable it will have to look something like (ax + b)(cx + d) where a*c = 8 and b*d = -5. This helps us out because now we know that either b or d must be negative, while a and c have to be something like 2 and 4, or -8 and -1. Since the middle term is a 3, you also know that a*d + b*c = 3. This gives enough information to try plugging in a few numbers and see what happens. We know either b or d are 1 and -5 or -1 and 5, so let's try the first set. (ax + 1)(bx - 5)....Hmmmm. Now let's use the other information at our disposal. -5a + b = 3 and a*b = 8. If you really get desperate, you can solve these equations or notice that if a = 1 and b = 8, then (x+1)(8x-5)=8x^2+3x-5. Bingo! If you really get stuck on any equation like ax^2+bx+c where a,b,c are just numbers, you can use the quadratic formula, which is a formula that will tell you the answers to the equation. The quadratic formula can be found in most textbooks. (I'd write it here, but I really don't think I could do it justice on this computer.) It's really helpful, especially if you get a really nasty polynomial... but remember it only works if x^2 is the largest power you're raising something to. If you have to deal with bigger polynomials, something like x^4 + 10x^3 + 8x^2 - 15, you have to use factor division, which is in most high school Algebra II books. If you've never seen a problem like the one I wrote down, don't worry about factor division; you might learn it next year in school. Good luck in your math classes next year in school. -Doctor Erich, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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