So to help illustrate some of the ideas were going to

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Unformatted text preview: tten in order of decreasing exponent. Also notice that any missing terms are acknowledged with a coefficient of zero. Now, it will probably be easier to write down the process and then explain it so here it is. The first thing we do is drop the first number in the top line straight down as shown. Then along each diagonal we multiply the starting number by r (which is 4 in this case) and put this number in the second row. Finally, add the numbers in the first and second row putting the results in the third row. We continue this until we get reach the final number in the first row. Now, notice that the numbers in the bottom row are the coefficients of the quadratic polynomial from our answer written order of decreasing exponent and the final number in the third row is the remainder. The answer is then the same as the first example. 5 x3 - x 2 + 6 = ( x - 4 ) ( 5 x 2 + 19 x + 76 ) + 310 We’ll do some more examples of synthetic division is a bit. However, we really should generalize things out a little first with the following fact. Division Algorithm Given a polynomial P(x) with degree at least 1 and any number...
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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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