Question

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

Answer 1

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

Answer 2

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

Answer 3

i am no good with division at all

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

list the coefficients of the numerator

1 8 -4 1 -2

Answer 8

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 \[x\]?

Answer 9

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

Answer 10

1?

Answer 11

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

Answer 12

8

Answer 13

yes, aka \[2^3\]

Answer 14

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

Answer 15

what do you mean without computing?

Answer 16

i mean write your answer as 5 to a power

Answer 17

not sure i follow...

Answer 18

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?

Answer 19

you should get x to a power yes?

Answer 20

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

Answer 21

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

Answer 22

=)

Answer 23

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

Answer 24

because we have a long division to do.

Answer 25

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

Answer 26

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 \[1^4=1\]!