## sara1234 3 years ago 1. Create your own third degree polynomial that when divided by x + 2 has a remainder of –4. 2. Create your own division of polynomials problem. Demonstrate how this problem would be solved using both long division and synthetic division.

1. dpaInc

what is the degree if you multiply x^2*(x+2) ?

2. dpaInc

\[\huge x^2(x+2) = \]

3. dpaInc

just multiply it out...

4. dpaInc

not quite... \[\large x^2(x+2)=x^3+2x \]... agreed?

5. sara1234

yes

6. dpaInc

so that's a third degree polynomial.. and what is the remainder if we take \(\large x^3+2x \) divided by \(\large x+2 \) ???

7. dpaInc

remember we just multiplied it out to get that third degree polynomial...

8. sara1234

-4

9. dpaInc

no...

10. sara1234

confused...................

11. dpaInc

if I ask you to multipl 2 times 3, what's the product?

12. dpaInc

**multiply...

13. sara1234

6

14. dpaInc

now... what's the remainder if I ask you 6 divided by 3 ?

15. sara1234

0

16. dpaInc

that's what i was asking in when we were working with the polynomial x^3 + 2x... the remainder when \(\large x^3+2x \) divided by \(\large x+2 \) is zero....

17. dpaInc

still with me?

18. sara1234

yeah

19. dpaInc

good... but we want a remainder of -4.... so what do you think we need to do?

20. sara1234

not sure

21. dpaInc

|dw:1340429487175:dw|

22. dpaInc

we need to stick something in that box so that our remainder is -4....

23. dpaInc

take a wild guess...

24. dpaInc

ok... how 'bout this....

25. sara1234

???

26. dpaInc

still there sara?

27. sara1234

yeah what goes in the box?

28. dpaInc

ok... sorry.. i made some typos up there... but this should be more clear...

29. dpaInc

|dw:1340430131260:dw|

30. dpaInc

|dw:1340430256983:dw|

31. dpaInc

see the question mark? what should it be in order for our remainder to be -4?

32. sara1234

-4

33. dpaInc

yes... i'm sorry i shuda done this way first.....

34. dpaInc

|dw:1340430491392:dw|

35. sara1234

okay gottcha thats the equation thats is a third degree polynomial that when divided by x + 2 has a remainder of –4. :)

36. dpaInc

yes...:) again.... sorry....

37. sara1234

its okay

38. dpaInc

thanks for sticking with me....:)