Concept of Factoring
Date: 03/22/97 at 13:22:54 From: James Torres Subject: Concept of Factoring My son is having problems with "factoring". I would like to know what he is talking about. Could you explain the concept of factoring and give examples of its practical uses? Thank you for your help, Jim Torres,
Date: 03/26/97 at 23:52:34 From: Doctor Jodi Subject: Re: Concept of Factoring Hi Jim, Thanks for your question. Factoring is an idea you might be somewhat familiar with from multiplication. The numbers multiplied together to get another number are its factors. For example, 4*3 = 12, so 3 and 4 are factors of 12. However, they're not its ONLY factors. 1, 2, 6, and 12 are other factors of 12. (Another way of defining a factor is a number which goes evenly into the number you're factoring.) The sort of factoring your son is doing is somewhat similar, but since it's algebra, there are probably LETTERS like x and y stuck into the equations. These letters just stand for UNKNOWNS. For example, you could have an equation like x + 1 = 5. You can ask yourself, what number, added to one, gives you five? X stands for that number. You could figure out the equation x + 1 = 5 by subtracting 1 from each side: x + 1 = 5 -1 -1 ----------- x = 4 Other algebraic equations (equations with letters) might look different, but the idea behind them is the same. So what does this have to do with factoring? Sometimes you'll have an equation that has a squared or cubed term which is unknown. Here's an example: x^2 = 9 Since the x is squared, there are TWO possible answers for x. You can probably guess that the answers will be -3 and 3, since -3 * -3 = 9 and 3 * 3 = 9. But suppose you don't know what the answer is (or suppose that you're dealing with a more complicated equation). How would you figure out what the answer is? Here's where we get back to factoring. Here's what you'd do: x^2 = 9 -9 -9 --------- x^2 - 9 = 0 Now, here's the trick. Remember, if you multiply 5 * 0, you get 0. In fact, if you multiply 28, or 1 billion, or any other number by 0, you get 0. And if you multiply and get 0 as an answer, at least one of the numbers you multiplied by MUST HAVE BEEN ZERO! We can use that fact here. We know that x^2 - 9 = 0. So one of the factors of x^2 - 9 must equal zero. Does that make sense? Next, we factor. Basically, this means saying to ourselves: What do we multiply to get x^2 - 9? There are a lot of tricks here, and I'm sure your son would be happy to show you some of them. From x^2 - 9 = 0, we get (x-3)(x+3) = 0. You could multiply this out and check it, but since factoring itself is the issue here, I won't. If you want help on that, ask your son, or write back to us. What it boils down to is breaking the equation into two parts (one for each of the two possibilities). Either x-3 could be zero or x + 3 could be zero. If x - 3 = 0, then + 3 + 3 ------------ x = 3. If x + 3 = 0, then - 3 - 3 ------------ x = - 3. I hope this isn't too overwhelming. I applaud your interest in the math your son is doing. Sometimes it's hard to stay involved in teenagers' life at school. Even though they may shrug when you ask what they did at school, or complain that you're too nosy, I think most teenagers will be glad that you take an interest in what they're doing. Too often, kids feel limited by the knowledge (or lack of knowledge) of their parents. Learning as much as you can--and being curious about their lives at school--really shows them how important learning is. Going out of your way to learn things that might be difficult at first also shows them how important they are to you. -Doctor Jodi, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.