Alg_Complete

We are doing this to make a point on how we can use

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Unformatted text preview: fy the second step we will use synthetic division. This will greatly simplify our life in several ways. First, recall that the last number in the final row is the polynomial evaluated at r and if we do get a zero the remaining numbers in the final row are the coefficients for Q ( x ) and so we won’t have to go back and find that. Also, in the evaluation step it is usually easiest to evaluate at the possible integer zeroes first and then go back and deal with any fractions if we have to. Let’s see how this works. Example 3 Determine all the zeroes of P ( x ) = x 4 - 7 x3 + 17 x 2 - 17 x + 6 . Solution We found the list of all possible rational zeroes in the previous example. Here they are. ±1, ± 2, ± 3, ± 6 We now need to start evaluating the polynomial at these numbers. We can start anywhere in the list and will continue until we find zero. To do the evaluations we will build a synthetic division table. In a synthetic division table do the multiplications in our head and drop the middle row just wr...
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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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