Question

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)

Answer 1

divide them in long division process

Answer 2

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

Answer 3

wait then

Answer 4

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

Answer 5

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....

Answer 6

ok so you know how to do long division yes?

Answer 7

first one is x^2+3x-5

Answer 8

don't just give answers lol

Answer 9

pls try second one on your own

Answer 10

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

Answer 11

ok

Answer 12

Yes I sort of know long division

Answer 13

your first term is x^4 right

Answer 14

yes i think so

Answer 15

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

Answer 16

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

Answer 17

we want to put polynomial in an ascending order

Answer 18

yes got it written down that way

Answer 19

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

Answer 20

what?

Answer 21

what?

Answer 22

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

Answer 23

then we put in long division

Answer 24

ok so you did this right?

Answer 25

so where did you find the problem? exactly

Answer 26

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

Answer 27

did you do this?

Answer 28

wait how did you do that?

Answer 29

i told you multiply it with x^2

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

ok. I sorta see that now.

Answer 34

this like you do with long division of numbers

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

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.

Answer 39

it is the same concept for all of them

Answer 40

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

Answer 41

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.

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

check lesson on exponents

Answer 46

or perhaps mathfoudantion by NJwildberger

Answer 47

foundation*

Answer 48

all those have lecture on those areas

Answer 49

ok, thanks.

Answer 50

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

Answer 51

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

Answer 52

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)

Answer 53

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

Answer 54

do you get my point

Answer 55

yes i see