Using synthetic division, what is the quotient: (x3 + 7x2 + 5x – 20) ÷ (x + 3) ?

- anonymous

Using synthetic division, what is the quotient: (x3 + 7x2 + 5x – 20) ÷ (x + 3) ?

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- amistre64

the quotient is what you end up with on the bottom i beleive

- amistre64

if your asking how to DO synthD thats a different can of worms

- angela210793

How do you do that amistre?

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## More answers

- 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

I was reading it on wikipedia but i didn't get it :(

- 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

the quotient is one degree less that what we started with; in this case we drop from x^3 to x^2

- angela210793

this is too complicated...long division method is better -_-

- amistre64

its complicated to expalin, its simple to do :)

- amistre64

you do all the parts of longhand ... so its not any more complicated, in fact its a smidge simpler

- amistre64

try it out, write out the coeffs in a row for me

- angela210793

|dw:1331733759955:dw|

- amistre64

then the next row is our addings; start it with a zero and underscore the whole thing

- amistre64

|dw:1331733747724:dw|

- angela210793

i didn't get smth tht ''r'' wht is it????

- 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

|dw:1331733866830:dw|

- angela210793

ahhhhhhhhhhhaaaaaaaaaaaaaaaa

- angela210793

|dw:1331733984298:dw|

- amistre64

add the first column .. 1+0 = 1
multiply that by 3 and add it to the next column ...

- amistre64

7+3 = 10, not 4

- angela210793

u add them :(((

- amistre64

|dw:1331733984083:dw|

- amistre64

we have a remainder left over; but the quotient is still the same; all the numbers up to the last column

- angela210793

|dw:1331734110667:dw|

- 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

so, quotient is:
x^2 +4x -7

- angela210793

Ohhhh......Thaaaaaaaaaaaaaaaaaaaaaanks a looooooooooooot Amistre :))))))))))))))))))))

- 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

Thanks :) for teaching me :))))
(even though i don't think I'll use it very often) :D
Thank you :)))

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