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)

- anonymous

- chestercat

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- madhu.mukherjee.946

divide them in long division process

- anonymous

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

- madhu.mukherjee.946

wait then

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## More answers

- xapproachesinfinity

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

- 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....

- xapproachesinfinity

ok so you know how to do long division yes?

- madhu.mukherjee.946

first one is x^2+3x-5

- xapproachesinfinity

don't just give answers lol

- madhu.mukherjee.946

pls try second one on your own

- anonymous

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

- madhu.mukherjee.946

ok

- anonymous

Yes I sort of know long division

- madhu.mukherjee.946

your first term is x^4 right

- anonymous

yes i think so

- xapproachesinfinity

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

- madhu.mukherjee.946

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

- xapproachesinfinity

we want to put polynomial in an ascending order

- anonymous

yes got it written down that way

- madhu.mukherjee.946

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

- anonymous

what?

- anonymous

what?

- madhu.mukherjee.946

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

- xapproachesinfinity

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

- xapproachesinfinity

ok so you did this right?

- xapproachesinfinity

so where did you find the problem? exactly

- anonymous

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

- xapproachesinfinity

|dw:1441770607055:dw|

- xapproachesinfinity

did you do this?

- anonymous

wait how did you do that?

- madhu.mukherjee.946

i told you multiply it with x^2

- anonymous

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

- 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

- 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

- anonymous

ok. I sorta see that now.

- xapproachesinfinity

this like you do with long division of numbers

- xapproachesinfinity

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

- xapproachesinfinity

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

- xapproachesinfinity

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

- 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.

- xapproachesinfinity

it is the same concept for all of them

- xapproachesinfinity

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

- 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.

- xapproachesinfinity

|dw:1441771163604:dw|

- 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

- anonymous

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

- xapproachesinfinity

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

- xapproachesinfinity

check lesson on exponents

- xapproachesinfinity

or perhaps mathfoudantion by NJwildberger

- xapproachesinfinity

foundation*

- xapproachesinfinity

all those have lecture on those areas

- anonymous

ok, thanks.

- xapproachesinfinity

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

- 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

- 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)

- xapproachesinfinity

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

- xapproachesinfinity

do you get my point

- anonymous

yes i see

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