DIVIDE RATIONAL EXPRESSIONS
(7r^3-24r^2-14r-8)/(r-4)
I totally forgot how to do this and cant find any good videos on this. Can anyone provide step by step instructions with explanations please!!?

- anonymous

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- freckles

Synthetic or long division?

- anonymous

I dont know it just says Perform the division

- freckles

So you don't care what method.

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## More answers

- freckles

I prefer synthetic then.

- freckles

|dw:1439675614505:dw|
this is the setup for the problem going with the synthetic approach

- freckles

you always bring down the first number inside (I just did 7+0)
|dw:1439675676233:dw|
whatever numbers you put below this bar gets multiply by that 4 number on the outside

- freckles

|dw:1439675710797:dw|

- freckles

add -24 and 28
then put that result underneath the bar (under the column that contains the -24 and 28)
and then multiply that result by 4

- freckles

|dw:1439675753198:dw|
try to continue the pattern

- freckles

4(4)=?

- anonymous

|dw:1439676022903:dw| like this? i've never done synthethic dvision before. sorry for the late reply

- freckles

well 4(4) should be 16

- freckles

|dw:1439676114092:dw|
but somehow you did -14+16 instead of -14+12 anyways

- freckles

so your division leads to 7x^2+4x+2

- freckles

oops x is r in this case

- freckles

|dw:1439676223679:dw|

- freckles

sometimes you might have to throw a 0 placeholder in there pretend we have
\[\frac{r^3+1}{r-1}\]
well r^3+1 is the same as r^3+0r^2+0r+1
so the setup would look like this
also the number that goes on the outside is 1 since the bottom is of the form r-1
if you have r-c then the outside number would be c
|dw:1439676430314:dw|
so the quotient is r^2+r+1 and the remainder is 2
or in other words
\[\frac{r^3+1}{r-1}=r^2+r+1+\frac{2}{r-1}\]

- freckles

example 2:
\[\frac{r^4+r}{r+5} \\ \]
r^4+r=r^4+0r^3+0r^2+1r+0
and since r+5=r-(-5) then the outside number is -5
|dw:1439676568491:dw|
so the quotient is r^3-5r^2+25r-124
and the remainder is 620
that is we can write
\[\frac{r^4+r}{r+5}=r^3-5r^2+25r-124+\frac{620}{r+5}\]

- freckles

synthetic division only works when the denominator can be expressed as x-c
and therefore as you noticed with the examples above the quotient will always be one degree less than the numerator of the division

- freckles

long division example:
|dw:1439676805835:dw|

- freckles

this is the setup for long divison
and yes I'm setting up your original problem

- freckles

I like to make sure the polynomial both inside and outside are in descending order otherwise it can get confusing

- freckles

these polynomials already good

- freckles

|dw:1439676887393:dw|
first question to ask yourself:
what is:
\[\frac{7r^3}{r} \\ \text{ well notice } r^3=r \cdot r^2 \\ \frac{7 r^2 \cdot r}{r} =7r^2\]
we put this number on top of the bar

- freckles

|dw:1439676965443:dw|

- freckles

whatever numbers we put up there we will multiply them once by (r-4)

- freckles

|dw:1439677015437:dw|
we subtract to see what is leftover

- freckles

\[(7r^3-24r^2)-(7r^3-28r^2) \\ (7r^3-7r^3)+(-24r^2+28r^2) \\ 0+4r^2 \\ 4r^2\]
this is the number we below that subtraction bar

- freckles

|dw:1439677114356:dw|
now we do the division again then multiplication then subtraction then repeat

- freckles

|dw:1439677147448:dw|
so we ask ourselves what is
\[\frac{4r^2}{r} \\ \text{ well notice } r^2=r \cdot r \\ \frac{4 r \cdot r}{r}=4r\]
4r is the number we put on the very top bar

- freckles

|dw:1439677205554:dw|
multiplication to the divisor (r-4)

- freckles

\[4r(r-4) \\ 4r(r-4)=4r^2-16r\]|dw:1439677247246:dw|

- freckles

and then we back to the subtraction

- freckles

|dw:1439677351500:dw|

- freckles

back to the division part |dw:1439677374516:dw|
what is 2r/r
this is 2

- freckles

|dw:1439677400999:dw|
then finally we done because there are no r's inside of 0
0 is the remainder
which means r-4 is a factor of the dividend which is 7r^3-24r^2-14r-8

- freckles

but yes this says
again \[\frac{7r^3-24r^2-14r-8}{r-4}=7r^2+4r+2\]

- freckles

synthetic division makes this slightly prettier and seems like less work :)

- freckles

I must go for now
peace and have fun

- anonymous

7r3âˆ’24r2âˆ’14râˆ’8 / râˆ’4
= 7r3âˆ’24r2âˆ’14râˆ’8 / râˆ’4
= (râˆ’4)(7r2+4r+2) / râˆ’4
=7r2+4r+2

- anonymous

Btw, r2 means r^2 :D

- anonymous

@freckles why didn't you divide the -4 in long division? is it only the variable that I have to divide?

- Nnesha

what -4 ? where is at ? :P

- Nnesha

ohh this one ?http://prntscr.com/85fre5

- Nnesha

ello r u there ?? o.O

- anonymous

also why is -24r^2 - 28r^2 positive? i got -52r^2

- anonymous

in long division

- anonymous

|dw:1439767178262:dw|

- anonymous

ooooooh no nvm

- Nnesha

remember you have to change the signs so
she changed negative to positive
that's how -24r^2+28r^2 =4r^2

- anonymous

yeah i see now thanks! :)

- Nnesha

|dw:1439767386640:dw|