First recall that the last number in the final row is

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Unformatted text preview: l be a factor of the appropriate number. © 2007 Paul Dawkins 263 College Algebra So, why is this theorem so useful? Well, for starters it will allow us to write down a list of possible rational zeroes for a polynomial and more importantly, any rational zeroes of a polynomial WILL be in this list. In other words, we can quickly determine all the rational zeroes of a polynomial simply by checking all the numbers in our list. Before getting into the process of finding the zeroes of a polynomial let’s see how to come up with a list of possible rational zeroes for a polynomial. Example 2 Find a list of all possible rational zeroes for each of the following polynomials. (a) P ( x ) = x 4 - 7 x3 + 17 x 2 - 17 x + 6 [Solution] (b) P ( x ) = 2 x 4 + x 3 + 3 x 2 + 3 x - 9 [Solution] Solution (a) P ( x ) = x 4 - 7 x3 + 17 x 2 - 17 x + 6 Now, just what does the rational root theorem say? It says that if x = b is to be a zero of P ( x ) c then b must be a factor of 6 and c must...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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