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anonymous
 one year ago
DIVIDE RATIONAL EXPRESSIONS
(7r^324r^214r8)/(r4)
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
 one year ago
DIVIDE RATIONAL EXPRESSIONS (7r^324r^214r8)/(r4) 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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freckles
 one year ago
Best ResponseYou've already chosen the best response.6Synthetic or long division?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I dont know it just says Perform the division

freckles
 one year ago
Best ResponseYou've already chosen the best response.6So you don't care what method.

freckles
 one year ago
Best ResponseYou've already chosen the best response.6I prefer synthetic then.

freckles
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439675614505:dw this is the setup for the problem going with the synthetic approach

freckles
 one year ago
Best ResponseYou've already chosen the best response.6you 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
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439675710797:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.6add 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
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439675753198:dw try to continue the pattern

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439676022903:dw like this? i've never done synthethic dvision before. sorry for the late reply

freckles
 one year ago
Best ResponseYou've already chosen the best response.6well 4(4) should be 16

freckles
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439676114092:dw but somehow you did 14+16 instead of 14+12 anyways

freckles
 one year ago
Best ResponseYou've already chosen the best response.6so your division leads to 7x^2+4x+2

freckles
 one year ago
Best ResponseYou've already chosen the best response.6oops x is r in this case

freckles
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439676223679:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.6sometimes you might have to throw a 0 placeholder in there pretend we have \[\frac{r^3+1}{r1}\] 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 r1 if you have rc 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 \[\frac{r^3+1}{r1}=r^2+r+1+\frac{2}{r1}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.6example 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^35r^2+25r124 and the remainder is 620 that is we can write \[\frac{r^4+r}{r+5}=r^35r^2+25r124+\frac{620}{r+5}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.6synthetic division only works when the denominator can be expressed as xc and therefore as you noticed with the examples above the quotient will always be one degree less than the numerator of the division

freckles
 one year ago
Best ResponseYou've already chosen the best response.6long division example: dw:1439676805835:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.6this is the setup for long divison and yes I'm setting up your original problem

freckles
 one year ago
Best ResponseYou've already chosen the best response.6I like to make sure the polynomial both inside and outside are in descending order otherwise it can get confusing

freckles
 one year ago
Best ResponseYou've already chosen the best response.6these polynomials already good

freckles
 one year ago
Best ResponseYou've already chosen the best response.6dw: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
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439676965443:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.6whatever numbers we put up there we will multiply them once by (r4)

freckles
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439677015437:dw we subtract to see what is leftover

freckles
 one year ago
Best ResponseYou've already chosen the best response.6\[(7r^324r^2)(7r^328r^2) \\ (7r^37r^3)+(24r^2+28r^2) \\ 0+4r^2 \\ 4r^2\] this is the number we below that subtraction bar

freckles
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439677114356:dw now we do the division again then multiplication then subtraction then repeat

freckles
 one year ago
Best ResponseYou've already chosen the best response.6dw: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
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439677205554:dw multiplication to the divisor (r4)

freckles
 one year ago
Best ResponseYou've already chosen the best response.6\[4r(r4) \\ 4r(r4)=4r^216r\]dw:1439677247246:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.6and then we back to the subtraction

freckles
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439677351500:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.6back to the division part dw:1439677374516:dw what is 2r/r this is 2

freckles
 one year ago
Best ResponseYou've already chosen the best response.6dw:1439677400999:dw then finally we done because there are no r's inside of 0 0 is the remainder which means r4 is a factor of the dividend which is 7r^324r^214r8

freckles
 one year ago
Best ResponseYou've already chosen the best response.6but yes this says again \[\frac{7r^324r^214r8}{r4}=7r^2+4r+2\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.6synthetic division makes this slightly prettier and seems like less work :)

freckles
 one year ago
Best ResponseYou've already chosen the best response.6I must go for now peace and have fun

anonymous
 one year ago
Best ResponseYou've already chosen the best response.07r3−24r2−14r−8 / r−4 = 7r3−24r2−14r−8 / r−4 = (r−4)(7r2+4r+2) / r−4 =7r2+4r+2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Btw, r2 means r^2 :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@freckles why didn't you divide the 4 in long division? is it only the variable that I have to divide?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1what 4 ? where is at ? :P

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1ohh this one ? http://prntscr.com/85fre5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0also why is 24r^2  28r^2 positive? i got 52r^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439767178262:dw

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.1remember you have to change the signs so she changed negative to positive that's how 24r^2+28r^2 =4r^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah i see now thanks! :)