anonymous
  • anonymous
Using synthetic division, what is the quotient: (x3 + 7x2 + 5x – 20) ÷ (x + 3) ?
Mathematics
schrodinger
  • schrodinger
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amistre64
  • amistre64
the quotient is what you end up with on the bottom i beleive
amistre64
  • amistre64
if your asking how to DO synthD thats a different can of worms
angela210793
  • angela210793
How do you do that amistre?

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amistre64
  • amistre64
the first thing I do is make sure I got all the exponents; you need a complete set in order to perform it proerly; any missing parts get zeroed out this is good tho: 3,2,1,0 is all there so strip the coeffs and their signs and put them in a row
angela210793
  • angela210793
I was reading it on wikipedia but i didn't get it :(
amistre64
  • amistre64
c1 c2 c3 c4 next we want a row that we will fill in to add these coeffs too; and start it with a 0 c1 c2 c3 c4 0 ------------- <--------------this next row we will fill in with the sums from the top and multiply them to our "root" c1 c2 c3 c4 0 ---------------- r ) c1 then we just follow thru like a synthD machine c1 c2 c3 c4 0 rc1 r(rc1+c2) r(r(rc1+c2)+c3) --------------------------------------- r ) c1 rc1+c2 r(rc1+c2)+c3 with any luck this is a 0 on the end, otherwise its the remainder the under side there is our quotient
amistre64
  • amistre64
the quotient is one degree less that what we started with; in this case we drop from x^3 to x^2
angela210793
  • angela210793
this is too complicated...long division method is better -_-
amistre64
  • amistre64
its complicated to expalin, its simple to do :)
amistre64
  • amistre64
you do all the parts of longhand ... so its not any more complicated, in fact its a smidge simpler
amistre64
  • amistre64
try it out, write out the coeffs in a row for me
angela210793
  • angela210793
|dw:1331733759955:dw|
amistre64
  • amistre64
then the next row is our addings; start it with a zero and underscore the whole thing
amistre64
  • amistre64
|dw:1331733747724:dw|
angela210793
  • angela210793
i didn't get smth tht ''r'' wht is it????
amistre64
  • amistre64
our "root" is going to be from the (x-3) = 0 part; our root is when x=3 so instead of subtracting our result as in longhand, we already take care of that by swapping signs from -3 to 3 and then add. root here = 3
amistre64
  • amistre64
|dw:1331733866830:dw|
angela210793
  • angela210793
ahhhhhhhhhhhaaaaaaaaaaaaaaaa
angela210793
  • angela210793
|dw:1331733984298:dw|
amistre64
  • amistre64
add the first column .. 1+0 = 1 multiply that by 3 and add it to the next column ...
amistre64
  • amistre64
7+3 = 10, not 4
angela210793
  • angela210793
u add them :(((
amistre64
  • amistre64
|dw:1331733984083:dw|
amistre64
  • amistre64
we have a remainder left over; but the quotient is still the same; all the numbers up to the last column
angela210793
  • angela210793
|dw:1331734110667:dw|
amistre64
  • amistre64
x3 + 7x2 + 5x – 20 ; opps, our divider is (x+3) :) so root is -3 lol x3 + 7x2 + 5x – 20 0 -3 -12 21 ------------------------- -3) 1 4 -7 R=1
amistre64
  • amistre64
so, quotient is: x^2 +4x -7
angela210793
  • angela210793
Ohhhh......Thaaaaaaaaaaaaaaaaaaaaaanks a looooooooooooot Amistre :))))))))))))))))))))
amistre64
  • amistre64
since the variables dont actually play into the process, they strip them; but i find it rather pointless to say they HAVE to not be there; it leads to confusion alot i think
angela210793
  • angela210793
Thanks :) for teaching me :)))) (even though i don't think I'll use it very often) :D Thank you :)))

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