anonymous one year ago Divide Polynomials? (27x^4-18x^3+9x^2)/3x

1. Nnesha

for 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

2. anonymous

can you show me how?

3. Nnesha

|dw:1441648360041:dw|

4. Nnesha

so divide first terms $\huge\rm \frac{ 27x^4 }{ 3x } =?$

5. anonymous

9x but what is the exponent rule?

6. anonymous

ok page works now. 9x3?

7. anonymous

?

8. Nnesha

when we divide same bases we should subtract their exponents or x^4 is same as x times x times x times $\huge\rm \frac{ 27 ⋅x ⋅x⋅x⋅x }{3⋅x}$

9. Nnesha

yes that's right now multiply the divisor by 9x^3

10. Nnesha

|dw:1441649011288:dw|

11. anonymous

so the final answer is 9x^3+6x^2+3x

12. Nnesha

9x^3 times 3x = 27x^4 and then change the sign first term would cancel out the repeat those steps |dw:1441649027500:dw|

13. Nnesha

show ur work plz :=0

14. Nnesha

:=)*

15. anonymous

Ok I see! Thanks!!! I assume multiplying is adding exponents so just the division in reverse?

16. Nnesha

yes right!

17. anonymous

thank you!

18. Nnesha

multiply same bases ADD exponents $\rm x^m \times x^n =x^{m+n}$ divide same bases subtract exponents $\rm \frac{ x^m }{x^n }=x^{m-n}$

19. Nnesha

yw!

20. anonymous

btw, what if there's more after the variable in the divisor. say 3x-2?

21. Nnesha

then you have to multiply by both terms like 9x^3(3x-2) 9x^3 times 3x - 9x^3 times -2

22. anonymous

what would 9x^3 times -2 look like

23. Nnesha

lets say |dw:1441649570148:dw|there is 3x-2

24. Nnesha

just multiply the coefficients$\huge\rm -9x^3 \times -2=(-9 \times -2)x^3$

25. anonymous

oh so just 18x3

26. Nnesha

yes right!

27. anonymous

but where do you go from there? how does it get to the next step?

28. Nnesha

just repeat the steps divide first terms multiply the result by the divisor change signs

29. anonymous

but what's the point of the -2 then? idk im confused. i guess where do you put the 18x3?

30. Nnesha

below the 2nd term

31. Nnesha

coefficients should be the same so 9x^3 times -2 = -18x^3 <--3rd degree so put under the x^3 term

32. anonymous

oh i see, it cancels out? so it's 9x^2 / 3x-2 now?

33. anonymous

ok i think i got it now.

34. Nnesha

no just divide first terms !

35. Nnesha

first term of polynomial by first term of divisor so it would be $\huge\rm \frac{ 9x^2 }{ 3x }$

36. anonymous

ok give me a second

37. Nnesha

ok!

38. anonymous

i have to go be back in a while

39. Nnesha

alright same here cya

40. anonymous

@nnesha are you still here? ok i was using 9x^3 as an example. the real problem is 6x^3+11x^2-4x-4 / 3x-2

41. Nnesha

same steps ;=)

42. Nnesha

so first terms are 6x^3 and first term of divisor is 3x divide 6x^3/3x