## anonymous one year ago 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!!?

1. freckles

Synthetic or long division?

2. anonymous

I dont know it just says Perform the division

3. freckles

So you don't care what method.

4. freckles

I prefer synthetic then.

5. freckles

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

6. 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

7. freckles

|dw:1439675710797:dw|

8. 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

9. freckles

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

10. freckles

4(4)=?

11. anonymous

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

12. freckles

well 4(4) should be 16

13. freckles

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

14. freckles

15. freckles

oops x is r in this case

16. freckles

|dw:1439676223679:dw|

17. 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 $\frac{r^3+1}{r-1}=r^2+r+1+\frac{2}{r-1}$

18. 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 $\frac{r^4+r}{r+5}=r^3-5r^2+25r-124+\frac{620}{r+5}$

19. 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

20. freckles

long division example: |dw:1439676805835:dw|

21. freckles

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

22. freckles

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

23. freckles

24. 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

25. freckles

|dw:1439676965443:dw|

26. freckles

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

27. freckles

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

28. 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

29. freckles

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

30. 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

31. freckles

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

32. freckles

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

33. freckles

and then we back to the subtraction

34. freckles

|dw:1439677351500:dw|

35. freckles

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

36. 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

37. freckles

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

38. freckles

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

39. freckles

I must go for now peace and have fun

40. anonymous

7r3−24r2−14r−8 / r−4 = 7r3−24r2−14r−8 / r−4 = (r−4)(7r2+4r+2) / r−4 =7r2+4r+2

41. anonymous

Btw, r2 means r^2 :D

42. anonymous

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

43. Nnesha

what -4 ? where is at ? :P

44. Nnesha

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

45. Nnesha

ello r u there ?? o.O

46. anonymous

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

47. anonymous

in long division

48. anonymous

|dw:1439767178262:dw|

49. anonymous

ooooooh no nvm

50. Nnesha

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

51. anonymous

yeah i see now thanks! :)

52. Nnesha

|dw:1439767386640:dw|