Factoring Polynomials with Common Expressions
Date: 08/20/2005 at 13:11:00 From: Eiven Subject: Algebra is too confusing!!!! Simplify 8(x-3) - 2(x-3)² A 2(x-3)(x-3) B 2(x-3)(x-7) C 2(x-3)(7-x) D 2(3-x)(7-x) This is one of the questions during a quiz. I can't seem to find the right answer. Here's what I've tried: = 8x - 24 - 2x² + 12x + 18 = 20x - 2x² - 6 = 2(x² + 10x - 3)
Date: 08/20/2005 at 13:44:47 From: Doctor Ian Subject: Re: Algebra is too confusing!!!! Hi Eiven, There is a hard way to do this, and an easy way. The hard way is to go ahead and expand everything: 8(x-3) - 2(x-3)^2 = (8x - 24) - 2(x^2 - 6x + 9) = (8x - 24) - (2x^2 - 12x + 18) = 8x - 24 - 2x^2 + 12x - 18 [Note the final sign] = 20x - 2x^2 - 42 = -2x^2 + 20x - 42 = -2(x^2 - 10x + 21) = -2(x - 7)(x - 3) = 2(7 - x)(x - 3) It looks like you were doing fine, but you missed a sign at one step. But here's an easier way to do it. Suppose we replace the expression (x-3) with a single variable, like u. Then we have 8u - 2u^2 = u(8 - 2u) = 2u(4 - u) Now we can undo the substitution by putting (x-3) back in for u: = 2(x - 3)(4 - (x - 3)) = 2(x - 3)(7 - x) That was a lot less work, huh? How did I do that? Well, whenever I see an expression that turns up in more than one place, like (x-3), I'll try replacing it with a single variable. That will let me spot patterns that are harder to see with all the expressions fully expanded. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 08/23/2005 at 03:07:05 From: Eiven Subject: Thank you (Algebra is too confusing!!!!) Thanks a lot. Your solution makes it look a lot easier to me.
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