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!!?

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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!!?

Mathematics
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Synthetic or long division?
I dont know it just says Perform the division
So you don't care what method.

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I prefer synthetic then.
|dw:1439675614505:dw| this is the setup for the problem going with the synthetic approach
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
|dw:1439675710797:dw|
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
|dw:1439675753198:dw| try to continue the pattern
4(4)=?
|dw:1439676022903:dw| like this? i've never done synthethic dvision before. sorry for the late reply
well 4(4) should be 16
|dw:1439676114092:dw| but somehow you did -14+16 instead of -14+12 anyways
so your division leads to 7x^2+4x+2
oops x is r in this case
|dw:1439676223679:dw|
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 \[\frac{r^3+1}{r-1}=r^2+r+1+\frac{2}{r-1}\]
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 \[\frac{r^4+r}{r+5}=r^3-5r^2+25r-124+\frac{620}{r+5}\]
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
long division example: |dw:1439676805835:dw|
this is the setup for long divison and yes I'm setting up your original problem
I like to make sure the polynomial both inside and outside are in descending order otherwise it can get confusing
these polynomials already good
|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
|dw:1439676965443:dw|
whatever numbers we put up there we will multiply them once by (r-4)
|dw:1439677015437:dw| we subtract to see what is leftover
\[(7r^3-24r^2)-(7r^3-28r^2) \\ (7r^3-7r^3)+(-24r^2+28r^2) \\ 0+4r^2 \\ 4r^2\] this is the number we below that subtraction bar
|dw:1439677114356:dw| now we do the division again then multiplication then subtraction then repeat
|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
|dw:1439677205554:dw| multiplication to the divisor (r-4)
\[4r(r-4) \\ 4r(r-4)=4r^2-16r\]|dw:1439677247246:dw|
and then we back to the subtraction
|dw:1439677351500:dw|
back to the division part |dw:1439677374516:dw| what is 2r/r this is 2
|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
but yes this says again \[\frac{7r^3-24r^2-14r-8}{r-4}=7r^2+4r+2\]
synthetic division makes this slightly prettier and seems like less work :)
I must go for now peace and have fun
7r3−24r2−14r−8 / r−4 = 7r3−24r2−14r−8 / r−4 = (r−4)(7r2+4r+2) / r−4 =7r2+4r+2
Btw, r2 means r^2 :D
@freckles why didn't you divide the -4 in long division? is it only the variable that I have to divide?
what -4 ? where is at ? :P
ohh this one ?http://prntscr.com/85fre5
ello r u there ?? o.O
also why is -24r^2 - 28r^2 positive? i got -52r^2
in long division
|dw:1439767178262:dw|
ooooooh no nvm
remember you have to change the signs so she changed negative to positive that's how -24r^2+28r^2 =4r^2
yeah i see now thanks! :)
|dw:1439767386640:dw|
np :)

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