1. Nnesha

long division 5 steps) $$\huge\color{green}{{1:}}$$ Divide the first terms $$\huge\color{green}{{2:}}$$ multiply(distribute) $$\huge\color{green}{{3:}}$$ subtract all terms $$\huge\color{green}{{4:}}$$ carry down $$\huge\color{green}{{5:}}$$ repeat |dw:1433974939206:dw|there isn't x^2 term in the question but we have to write it in order 3 2 1 0 like this

2. Loser66

I believe the problem is "simplify" instead of "solve"

3. Nnesha

divide first terms $\rm \frac{ -18x^3 }{ 3x } = ??$

4. anonymous

=-6x^3? @Nnesha

5. Nnesha

x^3 can be written as x times x times x so $\rm \frac{ x \times x \times x }{ x } = ??$

6. anonymous

x^3? @Nnesha

7. Nnesha

nope you can cancel one x right ?

8. Nnesha

$\rm \frac{ x \times x \times \cancel x }{ \cancel x } = ??$

9. anonymous

Ok! So x^2? @Nnesha

10. Nnesha

yes right!

11. Nnesha

now 2nd step |dw:1433975352357:dw| distribute divisor by -6x^2 so -6x^2 (3x+2)

12. anonymous

So -18x^2 +4? @Nnesha

13. Nnesha

nope when you multiply same bases you should add their exponents

14. anonymous

I understand. So 18x^3+4 @Nnesha

15. Nnesha

distribute meaning multiply everything which is inside the parentheses by outside term so -6x^2 (3x+2) -6x^2 times 3x = ?? -6x^2 times 2 =?

16. Nnesha

yes x^3 is right but there is a little mistake :-)

17. anonymous

So 18x^3 and 12x^2? @Nnesha

18. Nnesha

you forgot negative sign

19. anonymous

Oh yeah! So -18x^3 and -12x^2? @Nnesha

20. Nnesha

there you go!

21. Nnesha

|dw:1433975913009:dw| step 3 change sign and then combine like terms :-)

22. anonymous

So 12x^2+17x+6? @Nnesha

23. Nnesha

yes right! now repeat!

24. Nnesha

|dw:1433976142678:dw| divide first terms 12x^2/3x

25. anonymous

Ok so 4x? @Nnesha

26. Nnesha

yep!

27. anonymous

And the next step is to divide 6 by 2? So would the answer be -6x^2+4x+3? @Nnesha

28. Nnesha

6 by 2 ??

29. Nnesha

4x right now 2nd step distribute!

30. anonymous

Sorry, I'm confused with what to do next. @Nnesha

31. Nnesha

1st step is divide you did that now 2nd step distribute 4x by divisor

32. anonymous

ok so do I divide 17x by 4x now? @Nnesha

33. Nnesha

alright nope you don't have to divide by quotient |dw:1433976642990:dw| divide first terms remember 3x stay same

34. Nnesha

you got 4x now distribute divisor by 4x 4x(3x+2) = ?

35. Nnesha

|dw:1433976698488:dw|

36. anonymous

So 12x+8x? @Nnesha

37. Nnesha

remember when you multiply same bases you should add their exponents so 4x times 3x = ?

38. anonymous

12x^2 @Nnesha

39. Nnesha

yep right :-)

40. Nnesha

|dw:1433976885337:dw| try!

41. anonymous

Ok so -6x^2+4x+3? @Nnesha

42. Nnesha

is that the quotient ?

43. anonymous

I think so @Nnesha

44. anonymous

Is that the correct answer? @Nnesha

45. Nnesha

is that a guess ?

46. anonymous

No, because I distributed 4x and I got 12x^2+8x+6 (I just left the 6 by itself) and then I divided that by 2 to simplify the answer. :) @Nnesha

47. Nnesha

alright |dw:1433977488813:dw| yes that's right 9x/3x = 3

48. anonymous

Ok is that all I had to do for that question? @Nnesha

49. Nnesha

that's just quotient what is the remainder answer should be like this $\large\rm qoutient + \frac{ remainder }{ divisor }$

50. anonymous

Oh. I'm not sure what the remainder/divisor would be. @Nnesha

51. Nnesha

|dw:1433977783733:dw| remainder that u get at the end after distributing 3 by divisor what did you get ?

52. Nnesha

|dw:1433977855878:dw| change sign at the end and then combine like terms what did yo uget

53. anonymous

I think I got 3? @Nnesha

54. Nnesha

nope that's the quotient |dw:1433977995683:dw|