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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!!?

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  1. freckles
    • one year ago
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    Synthetic or long division?

  2. anonymous
    • one year ago
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    I dont know it just says Perform the division

  3. freckles
    • one year ago
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    So you don't care what method.

  4. freckles
    • one year ago
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    I prefer synthetic then.

  5. freckles
    • one year ago
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    |dw:1439675614505:dw| this is the setup for the problem going with the synthetic approach

  6. freckles
    • one year ago
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    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
    • one year ago
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    |dw:1439675710797:dw|

  8. freckles
    • one year ago
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    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
    • one year ago
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    |dw:1439675753198:dw| try to continue the pattern

  10. freckles
    • one year ago
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    4(4)=?

  11. anonymous
    • one year ago
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    |dw:1439676022903:dw| like this? i've never done synthethic dvision before. sorry for the late reply

  12. freckles
    • one year ago
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    well 4(4) should be 16

  13. freckles
    • one year ago
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    |dw:1439676114092:dw| but somehow you did -14+16 instead of -14+12 anyways

  14. freckles
    • one year ago
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    so your division leads to 7x^2+4x+2

  15. freckles
    • one year ago
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    oops x is r in this case

  16. freckles
    • one year ago
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    |dw:1439676223679:dw|

  17. freckles
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    long division example: |dw:1439676805835:dw|

  21. freckles
    • one year ago
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    this is the setup for long divison and yes I'm setting up your original problem

  22. freckles
    • one year ago
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    I like to make sure the polynomial both inside and outside are in descending order otherwise it can get confusing

  23. freckles
    • one year ago
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    these polynomials already good

  24. freckles
    • one year ago
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    |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
    • one year ago
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    |dw:1439676965443:dw|

  26. freckles
    • one year ago
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    whatever numbers we put up there we will multiply them once by (r-4)

  27. freckles
    • one year ago
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    |dw:1439677015437:dw| we subtract to see what is leftover

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

  29. freckles
    • one year ago
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    |dw:1439677114356:dw| now we do the division again then multiplication then subtraction then repeat

  30. freckles
    • one year ago
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    |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
    • one year ago
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    |dw:1439677205554:dw| multiplication to the divisor (r-4)

  32. freckles
    • one year ago
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    \[4r(r-4) \\ 4r(r-4)=4r^2-16r\]|dw:1439677247246:dw|

  33. freckles
    • one year ago
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    and then we back to the subtraction

  34. freckles
    • one year ago
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    |dw:1439677351500:dw|

  35. freckles
    • one year ago
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    back to the division part |dw:1439677374516:dw| what is 2r/r this is 2

  36. freckles
    • one year ago
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    |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
    • one year ago
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    but yes this says again \[\frac{7r^3-24r^2-14r-8}{r-4}=7r^2+4r+2\]

  38. freckles
    • one year ago
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    synthetic division makes this slightly prettier and seems like less work :)

  39. freckles
    • one year ago
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    I must go for now peace and have fun

  40. anonymous
    • one year ago
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    7r3−24r2−14r−8 / r−4 = 7r3−24r2−14r−8 / r−4 = (r−4)(7r2+4r+2) / r−4 =7r2+4r+2

  41. anonymous
    • one year ago
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    Btw, r2 means r^2 :D

  42. anonymous
    • one year ago
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    @freckles why didn't you divide the -4 in long division? is it only the variable that I have to divide?

  43. Nnesha
    • one year ago
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    what -4 ? where is at ? :P

  44. Nnesha
    • one year ago
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    ohh this one ? http://prntscr.com/85fre5

  45. Nnesha
    • one year ago
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    ello r u there ?? o.O

  46. anonymous
    • one year ago
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    also why is -24r^2 - 28r^2 positive? i got -52r^2

  47. anonymous
    • one year ago
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    in long division

  48. anonymous
    • one year ago
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    |dw:1439767178262:dw|

  49. anonymous
    • one year ago
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    ooooooh no nvm

  50. Nnesha
    • one year ago
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    remember you have to change the signs so she changed negative to positive that's how -24r^2+28r^2 =4r^2

  51. anonymous
    • one year ago
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    yeah i see now thanks! :)

  52. Nnesha
    • one year ago
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    |dw:1439767386640:dw|