## anonymous one year ago Please help me with 3 Polynomial Q's? Last 3 in Quiz. (2x^3+x^4-6x^2+11x-10)/(x^2+2-x) (x^5-10x^2-8)/(x-2) (x^2+81)/(x+3)

divide them in long division process

2. anonymous

I know but I can't make it work with these problems.

wait then

4. xapproachesinfinity

why you can't make it work what is different?

5. anonymous

IDK why. I guess I don't understand it entirely? But with the latter two problems the answer is supposed to be relly long and it's a short problem....

6. xapproachesinfinity

ok so you know how to do long division yes?

first one is x^2+3x-5

8. xapproachesinfinity

pls try second one on your own

10. anonymous

I don't just want the answer. I want the problem explained. I want to be able to understand it .

ok

12. anonymous

Yes I sort of know long division

your first term is x^4 right

14. anonymous

yes i think so

15. xapproachesinfinity

first rewrite that as (x^4+2x^3-6x^2+11x-10)/(x^2-x+2)

okay now you see your divisor its x^2-x+2

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we want to put polynomial in an ascending order

18. anonymous

yes got it written down that way

x^2*x^2 =x^4 which is matching with your first term

20. anonymous

what?

21. anonymous

what?

so now multiply the entire x^2-x+2 with x^2

23. xapproachesinfinity

then we put in long division |dw:1441770468769:dw|

24. xapproachesinfinity

ok so you did this right?

25. xapproachesinfinity

so where did you find the problem? exactly

26. anonymous

yes it is in that form. the problem is from my online school quiz

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|dw:1441770607055:dw|

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did you do this?

29. anonymous

wait how did you do that?

i told you multiply it with x^2

31. anonymous

how does that work though! i'm completely clueless here....

32. xapproachesinfinity

well there an x^4 how to obtain that if you multiply by x^2 so you need an x^2 since x^2times x^2=x^4 we mainly focus on the leading terms

33. xapproachesinfinity

the divisor (x^2-x+2) has a leading term of x^2 the one we want to divide has a leading term of x^4

34. anonymous

ok. I sorta see that now.

35. xapproachesinfinity

this like you do with long division of numbers

36. xapproachesinfinity

we mainly focus on the first number yes! so here we look at the highest power (leading term)

37. xapproachesinfinity

that's why it is important to put the terms in order

38. xapproachesinfinity

ok now proceed what you need to do you said you have dealt with long division before

39. anonymous

yup, now that i've had help getting it started it's going good. may still need help with the other two in a bit.

40. xapproachesinfinity

it is the same concept for all of them

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for second you have x^5 what you need to multiply x by to get x^5?

42. anonymous

i know but the exponents are confusing me. everything i've done before had consecutivee numbers like 4,3,2. this is 5,2 etc.

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|dw:1441771163604:dw|

44. xapproachesinfinity

well may be you need to relook at how you deal with exponents because if you didn't solve that problem you will always run into it again

45. anonymous

yeah i know. any online source you can link me to?

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there are lot of good sources, look at PatrickJMT channel in youtube or khan academy, ProfRobBob

47. xapproachesinfinity

check lesson on exponents

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or perhaps mathfoudantion by NJwildberger

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foundation*

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all those have lecture on those areas

51. anonymous

ok, thanks.

52. xapproachesinfinity

look at them and do some problem tell you master the concept then you ready to move on and deal with polynomial easily

53. xapproachesinfinity

three properties you need to keep with you $$a^n\times a^m=a^{n+m}$$ $$\Large \frac{a^n}{a^m}=a^{n-m}$$ $$\frac{1}{a^n}=a^{-n}$$ these play a key role i lot of mathematics areas

54. xapproachesinfinity

when you deal x it is no different it is still the same properties applied over an over we just change variable. mathematics we don't mainly focus on the variable what is it rather we look at concepts (definition, theorem, etc)

55. xapproachesinfinity

so if i have x^3.x^2=x^{3+2}=x^5

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do you get my point

57. anonymous

yes i see