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My class has just been taught about polynomial division, and how it can be used to see if something is a factor (although remainder theorem is quicker), if the remainder = 0.

But what is the use of remainder that does not equal 0, I'm unsure where to apply this to in situations.

For example if you do:

$$\frac{3x^3+5x^2+x+4}{x-2}$$

the remainder is $50$, which means (more on the graphic side of things), that the line $x=2$ will intercept $3x^3+5x^2+x+4$ at $(2,50)$

But what use is this beyond "find the intercept", "find the remainder"?

(Like how you can ask "5 - 0.2 = ?", but a situation you apply that to, could be: "what is the change from a £5 note used to buy a 20p pencil")

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    If the remainder from dividing $f(x)=3x^3+5x^2+x+4$ by $x-2$ is $50$, then $f(2)=50$. Synthetic division is useful for evaluating polynomials quickly; the method is often associated with the name of Horner.2011-11-19
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    @J.M. Oh! I had thought it was the other way round, that explains a lot :)2011-11-19
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    @Jonathan How do you calculate something like $\int \frac{3x^3+5x^2+x+4}{x-2} dx$?2011-11-19

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