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I know how to do synthetic division, but I do not understand why it works.

Rachel
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  • Compare it with long division. All of the intermediate numbers should show up in both. – abnry Feb 09 '15 at 01:12
  • Ok. But I don't really understand how ling division works with polynomials – Rachel Feb 09 '15 at 01:15
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    Synthetic division is just a nice way of writing long division (you're basically omitting the $x$'s, and ignoring the terms you already know will cancel.) In order to understand why it works, you first need to understand how and why long division works. – hasnohat Feb 09 '15 at 01:18
  • Do you understand ordinary long division? It's hard to write up long division problems here. – abnry Feb 09 '15 at 01:21
  • Yes. I understand ordinary long division. But not with polynomials – Rachel Feb 09 '15 at 01:24
  • might help: http://math.stackexchange.com/questions/171191/why-does-synthetic-division-work?rq=1 – Sujaan Kunalan Feb 09 '15 at 01:25

1 Answers1

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Lets see a simple example:

$$x+1|x^2+2x+1$$

In order to do this using long polynomial division we do:

$$ \begin{array}{rl} \underline{x+1\phantom{00000}} & \hbox{} \\[-5pt] x + 1 | x^2+2x+1 \\ \underline{x^2+x\phantom{)))))}} & \hbox{($x \times x+1 = x^2+x$)} \\ x+1\phantom{} & \hbox{($(x^2 + 2x)- (x^2+x) = x$)} \\ \underline{\phantom{0}x+1\phantom{}} & \hbox{($(x+1)-(x+1) = 0$)} \\ \phantom{0}0 \end{array} $$

When we synthetic division we don't put in the x's to simplify it. (I want to do the synthetic division here but it takes really long to type)

Victor
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