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.

- anonymous

- katieb

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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.

- anonymous

yeah!

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## More answers

- anonymous

alright, is there another way to do this though rather than to divide all the time?

- anonymous

an easier solution or something?

- hba

@kerribaberri This is the easiest method on earth if you learn it
The easiest and the fastest :)

- anonymous

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

- anonymous

okay so we multiply everything by the 1, yes?

- hba

Yeah

- anonymous

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 ?

- anonymous

yes, i did.

- anonymous

is it usually the opposite? so instead of -1 it is 1?

- anonymous

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 ?

- anonymous

ahh, i see okay

- anonymous

then the last step after that would be (p + k - 1 + 3) ?

- hba

|dw:1353960431384:dw|
Yeah right :D
Shall i continue ?

- anonymous

:D sure

- hba

|dw:1353960534857:dw|
We will always seprate the last number :)

- hba

I know you will ask why ? right ?

- hba

@kerribaberri ?

- anonymous

yeah, why? :P

- anonymous

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 ?

- anonymous

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

@kerribaberri ??

- anonymous

yup :)

- anonymous

yeah, i got it. :)

- hba

I can replace R(x) with p+k-1+3
so
p+k+2=4
got it @kerribaberri ?

- anonymous

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 :)

- anonymous

so 2 goes on the left..

- hba

Yeah start doing it in the diag

- anonymous

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

- anonymous

okayy

- anonymous

LOL did i pick the correct numbers though?

- anonymous

|dw:1353961667693:dw|

- hba

Where did -2 and +2 come from ?

- anonymous

|dw:1353961803438:dw|

- anonymous

i took the 2 from the equation and.. ohhhhhhh am i supposed to multiply -2 by 3?

- anonymous

ohhhh wait, i didn't realize the 3 and the 2 were exponents..

- anonymous

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.

- anonymous

okay i got it..

- anonymous

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 ?

- anonymous

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|

- anonymous

ohhh, i never thought that was an option

- hba

Are you solving it now lol ?

- anonymous

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

- anonymous

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 ?

- anonymous

i'll just ask someone else LOL

- hba

No i am showing you wait.

- anonymous

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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