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

1. amistre64

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

2. amistre64

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

3. angela210793

How do you do that amistre?

4. 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

5. angela210793

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

6. 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

7. amistre64

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

8. angela210793

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

9. amistre64

its complicated to expalin, its simple to do :)

10. amistre64

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

11. amistre64

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

12. angela210793

|dw:1331733759955:dw|

13. amistre64

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

14. amistre64

|dw:1331733747724:dw|

15. angela210793

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

16. 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

17. amistre64

|dw:1331733866830:dw|

18. angela210793

ahhhhhhhhhhhaaaaaaaaaaaaaaaa

19. angela210793

|dw:1331733984298:dw|

20. amistre64

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

21. amistre64

7+3 = 10, not 4

22. angela210793

23. amistre64

|dw:1331733984083:dw|

24. amistre64

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

25. angela210793

|dw:1331734110667:dw|

26. 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

27. amistre64

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

28. angela210793

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

29. 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

30. angela210793

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