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when kx3 + px2 - x + 3 is divided by x - 1, the remainder is 4. When kx3 + px2 is divided by x - 2, the remainder is 21. Find the values of k and p.

Mathematics
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  • hba
|dw:1353959611123:dw| got this part ?
  • hba
Lets do this fast @kerribaberri Just tell me if you do not understand.
yeah!

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Other answers:

alright, is there another way to do this though rather than to divide all the time?
an easier solution or something?
  • hba
@kerribaberri This is the easiest method on earth if you learn it The easiest and the fastest :)
alright! let's do this LOL
  • hba
|dw:1353959860849:dw| We take the k down.
  • hba
|dw:1353959905760:dw| We multiply the k by 1 k*1=k
  • hba
|dw:1353959933565:dw| We multiply it and put it there,following me @kerribaberri
okay so we multiply everything by the 1, yes?
  • hba
Yeah
why is it just 1 rather than x - 1?
  • hba
|dw:1353960062608:dw| We add p and q so we get p+q now and then multiply it by 1
  • hba
In this method we take x-1 put it equal to 0 so x-1=0 x=1 So we have to put this .
  • hba
Did you get my step above shown in the diag ?
yes, i did.
is it usually the opposite? so instead of -1 it is 1?
so if i was to be given x - 3, it would be divided all by 3?
  • hba
|dw:1353960245291:dw| here we have added (p+q)+(-1)=p+q-1 and then multiply it by 1
  • hba
@kerribaberri Yeah you are right but if the question come 2x-2=0 then 2x=2 x=1
  • hba
Did you get my step above ?
ahh, i see okay
then the last step after that would be (p + k - 1 + 3) ?
  • hba
|dw:1353960431384:dw| Yeah right :D Shall i continue ?
:D sure
  • hba
|dw:1353960534857:dw| We will always seprate the last number :)
  • hba
I know you will ask why ? right ?
  • hba
yeah, why? :P
i was wondering why there was a line in between
  • hba
|dw:1353960695933:dw| Here P(x)=polynomial of x and R(x)=remainder of x So we seprate them ,Got it @kerribaberri ?
ohhh okay i get it @hba
  • hba
We have been provided in the question that the remainder is 4 so R(x)=4 got it ?
  • hba
yup :)
yeah, i got it. :)
  • hba
I can replace R(x) with p+k-1+3 so p+k+2=4 got it @kerribaberri ?
yes @hba
  • hba
so p+k=4-2 p+k=2
  • hba
Now lets solve the other one.|dw:1353961284346:dw| Your turn @kerribaberri Do it i'll help you where you go wrong :)
so 2 goes on the left..
  • hba
Yeah start doing it in the diag
k p -2 2 ? o_O
  • hba
Do it in the diag lol
  • hba
Do you see a pencil on my diag press it and start working
1 Attachment
okayy
LOL did i pick the correct numbers though?
|dw:1353961667693:dw|
  • hba
Where did -2 and +2 come from ?
|dw:1353961803438:dw|
i took the 2 from the equation and.. ohhhhhhh am i supposed to multiply -2 by 3?
ohhhh wait, i didn't realize the 3 and the 2 were exponents..
i thought they were base numbers
  • hba
The equation in the first thing was kx3 + px2 - x + 3 so i got k p -1 3 In the second case the equation iss kx^3+px^2 so you should get k p right ?
  • hba
|dw:1353962035949:dw||dw:1353962058098:dw|
  • hba
Got it ?
  • hba
@kerribaberri Please concentrate Its easy.
okay i got it..
i see where the k and p are coming from but i don't see where the last two come from
  • hba
|dw:1353962174399:dw| Now continue
  • hba
|dw:1353962211804:dw|
  • hba
Got where the last two came from ?
yeah i see it there because there are numbers, but this one has none?
  • hba
So you do not have to write anything.
  • hba
|dw:1353962420562:dw|
ohhh, i never thought that was an option
  • hba
Are you solving it now lol ?
r(x) = 21
  • hba
@kerribaberri Please try.
  • hba
@kerribaberri First solve it lol
  • hba
|dw:1353962559852:dw| bring the k down multiply it by 2
if there's no numbers|dw:1353962609644:dw|
  • hba
What is wrong with you ?
  • hba
The method is bring the k down multiply i by 2 so it will become 2k then it will go under p
  • hba
@kerribaberri Please try to understand i feel like slamming my head in the wall.
  • hba
@kerribaberri You there ?
i'll just ask someone else LOL
  • hba
No i am showing you wait.
No you are not..
  • hba
|dw:1353963033373:dw|
  • hba
So, R(x)=21 2x+p=21 got it ?
  • hba
|dw:1353963147883:dw|
  • hba
|dw:1353963244019:dw|
  • hba
@kerribaberri got it ?

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