- anonymous

Use long division to perform the division (Express your answer as quotient + remainder/divisor.)

- schrodinger

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- anonymous

\[x^4+8x^3-4x^2+x-2 \over x-2\]

- anonymous

do you know how to use 'synthetic division'? i can try to write it if you do not

- anonymous

i am no good with division at all

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## More answers

- anonymous

oh actually it says "long division" doesn't it. ok then take out paper and pencil and write like you would a regular long division problem
\[x-2|x^4+8x^3-4x^2+x-2\]

- anonymous

something like that. or would you just like to use synthetic division it is much much easier.

- anonymous

i believe it wants me to work it out the way you wrote it up top

- anonymous

list the coefficients of the numerator
1 8 -4 1 -2

- anonymous

ok they we are in for a world of annoyance. fine, write what i did first. now forget about the -4 for a moment. what is \[x^4\] divided by \[x\]?

- anonymous

in other words how many times does \[x\] go in to \[x^4\] or even more simply what is \[\frac{x^4}{x}\]?

- anonymous

1?

- anonymous

no, try this. what is
\[\frac{2^4}{2}\]?

- anonymous

8

- anonymous

yes, aka \[2^3\]

- anonymous

what do you think \[\frac{5^4}{5}\] is without computing

- anonymous

what do you mean without computing?

- anonymous

i mean write your answer as 5 to a power

- anonymous

not sure i follow...

- anonymous

ok lets try this
\[\frac{x^4}{x}=\frac{x\times x \times x\times x}{x}\] and when you cancel one of the x's what do you get?

- anonymous

you should get x to a power yes?

- anonymous

Or you can think of it as "What do I need to multiply times x to get \(x^4\)"

- anonymous

polpak you get the award for the day with \[b^0\]!

- anonymous

=)

- anonymous

now lets see if we (you) can help mathater realize that \[\frac{x^4}{x}=x^?\]

- anonymous

because we have a long division to do.

- anonymous

I don't think it'll work cause they're not here anymore ;)

- anonymous

yes, the problem is variables are confusing if you are not used to them. that is why
\[\frac{x^4}{x}=1\] cancel the x's and \[1^4=1\]!

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