1. anonymous

@jim_thompson5910

2. anonymous

3. jim_thompson5910

I think you meant to write \[\Large (x-3)^5\] ??

4. anonymous

I didn't write it, that's the problem, but ya that's what it is

5. jim_thompson5910

ah I see

6. jim_thompson5910

|dw:1434074979018:dw|

7. jim_thompson5910

|dw:1434074990114:dw|

8. jim_thompson5910

|dw:1434075006325:dw|

9. anonymous

ok

10. jim_thompson5910

what I'm going to do is write out 6 rows of (x) and (-3) put together, but with a bit of space between them I'm doing 6 because the degree is 5, so there are 5+1 = 6 terms total |dw:1434075073618:dw|

11. anonymous

oh ok

12. jim_thompson5910

the exponent for the x in row 1 will be 5, we start with the degree |dw:1434075149089:dw|

13. jim_thompson5910

the exponent over -3 will be 0 we want the exponents for x and -3 to always add to 5 |dw:1434075177797:dw|

14. jim_thompson5910

the x exponents will count down to 0 the -3 exponents will count up to 5 |dw:1434075199450:dw|

15. jim_thompson5910

notice how each pair of exponents add back up to 5 eg: 3+2 = 5 |dw:1434075236860:dw|

16. anonymous

ya ok

17. jim_thompson5910

the last thing needed are the binomial coefficients

18. jim_thompson5910

we get those from pascals triangle or from the combination formula n C r

19. anonymous

ok

20. jim_thompson5910

http://mathforum.org/workshops/usi/pascal/images/pascal.hex2.gif what are the numbers in the row that has "1, 5, ..."

21. anonymous

1, 5, 10, 10, 5, 1

22. jim_thompson5910

arrange those numbers vertically like so |dw:1434075368092:dw|

23. jim_thompson5910

the next step is to simplify each row in the drawing to get the 6 terms then you add up the 6 terms to get the overall polynomial

24. anonymous

ok

25. anonymous

26. jim_thompson5910

I'll be right back

27. anonymous

ok

28. anonymous

I have to finish this really soon... we're so close to being done!

29. anonymous

I have to be done, its my last problem I'll get a little credit I'm turning it in how it is. thank you SO MUCH for all your help @jim_thompson5910 !

30. jim_thompson5910

I'm back. Sorry about that but I'm glad it's making sense now