Polynomial ProblemDate: 11 Mar 1995 16:21:18 -0500 From: Anonymous Subject: Algebra II Anna-Jonesboro needs your help again. The problem is: A remainder of 9 results when the polynomial p(x) is divided by x - 2. A remaimder of -3 results when p(x) is divided by x + 2. A remainder of 3 results when p(x) is divided by x - 1. Find the remainder when p(x) is divided by (x - 2)(x + 2)(x - 1). Could you just give us a hint first? Ruth Roy A-J. Date: 23 Mar 1995 00:50:39 -0500 From: Dr. Ken Subject: Re: Algebra II Hey folks, It's Ethan and after a little discussion with my friend Ken, and a little help from a professor here we got it. The idea is really neat. Here is the hint. I will start with a pretty vague hint and if you need more then write back. All right we have this function and we want to know the remainder when we divide by that product. I think that it will be easier if we just think of it as trying to find the smallest polynomial that we can that has the given properties. That will be the remainder. Okay so here is the process. It may not make sense to you because I don't want to give away too much. Let us call f(x) our function. Well then if f(x)/x-2 has remainder 9 then f(2) must be nine. Similarly f(-2) = -3 AND F(1) = 3 I will let you think about why that is true since you said that you just wanted a hint. I will also let you think about how we can use this fact to find the answer. Write back if this isn't enough of a hint. Ethan Doctor On Call -Ken "Dr." Math |
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