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Dividing two Polynomials

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From: Anonymous
Date: Fri, 28 Jun 1996 9:22:58 -0400 (EDT)
Subject: Find all the integer values of X

I don't understand this problem. Can you help me?

Find all the integer values of X for which
12(x^2 - 4x + 3) / x^3 - 3x^2 -x >+ 3 has a
positive integer value.
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Date: Fri, 28 Jun 1996 13:33:35 -0400 (EDT)
From: Dr. Anthony
Subject: Find all the integer values of X

We start by simplifying the given expression:

= 12(x-1)(x-3)/{(x-1)(x+1)(x-3)}

= 12/(x+1) But x=1 and x=3 will produce 0/0 for the expression,
meaning that it could take all possible values.

We also have 12/(x+1) = k where k can take values 1, 2, 3, etc., etc.

k=1 gives x+1 = 12 so x = 11, so for k=1 we could have x = 1, 3, 11

k=2 gives x+1 = 6 so x = 5, and for k=2 we could have x = 1, 3, 5

k=3 gives x+1 = 4 so x = 3 and for k=3 we could have x = 1, 3

k=4 gives x+1 = 3 so x = 2 and for k=4 we could have x = 1, 2, 3

k=5 gives no further solution apart from x = 1, 3

k=6 gives x+1=2 so x = 1 and for k=6 we could have x = 1, 3

For k>6 only solutions will be x = 1, 3

-Doctor Anthony, The Math Forum

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Associated Topics:
High School Polynomials

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