Question

when p(x)=x^2 + ax -b is divided by x-1, the remainder is 6. when p(x) is divided by x+2. the remainder is 3. find the values of a and b.

Answer 1

Combines polynomials with systems of linear equations.
Like I told Faye, the way to get the remainder when f(x) is divided by (x-c) is to simply plug in c into the function.
IE
Remainder of p(x) when it's divided by x-1... is just p(1)
So... what is p(1)

Answer 2

x-c

Answer 3

wth?

Answer 4

p(x)=x^2+ax-b

Answer 5

mhmm
so
p(1) = ?

Answer 6

i was just asking what x-c is.

Answer 7

Just an example.

Answer 8

oh. xDD

Answer 9

Or, a formula.
In this case, x-c is x-1

Answer 10

So, c=1
now just plug in 1 into the function p(x) = x² + ax - b

Answer 11

okaay,, p(1)=(1)^2+a(1)-b

Answer 12

after that??

Answer 13

Simplify -.-
1² + a(1) - b
= 1 + a - b
Okay, and this is equal to -6, as per the given.
-6 = a - b + 1

Answer 14

sorry,, typo,, its not -6 its only 6

Answer 15

hmm...
6 = a - b + 1
Understood?

Answer 16

Or, simplify further, we get
a - b = 5

Answer 17

... stay with me here...

Answer 18

why 6 = a - b + 1??? where did you get +1??

Answer 19

Focus... since the remainder of p(x) when it's divided by x-1 is 6, it can only mean that
p(1) = 6
p(1) = 1² + a(1) - b = 1 + a - b
etc

Answer 20

ahah, xDD sorry,, didn't see thatxDD

Answer 21

after that??

Answer 22

You know a-b = 5
That's not enough to know the value of a and b, you need another equation.

Now that we mention it... we have another fact... that when it's divided by x + 2, the remainder is 3.
Can only mean that p(-2) = 3
Solve this part.

Answer 23

Hey... p(-2)... what is it?

Answer 24

huh??

Answer 25

sorry,, we just started doing that today, xDD

Answer 26

No better time than now.
It's just plugging in x = -2... how hard can it be? :P
p(-2) = ?

Answer 27

p(-2)=(-2)^2+a(-2)-b

Answer 28

simplify...

Answer 29

4-2a-b

Answer 30

And this is equal to...?

Answer 31

2a-b=-4

Answer 32

Excuse me...?

Answer 33

my eyes hurts,.. T_T

Answer 34

-.-
my eyes *hurt*
and anyway...
you're losing focus...

Answer 35

-2a-b=4

Answer 36

Don't you just hate it when the other kid gets the right answer and then 'corrects' it with an incorrect one -.-

Answer 37

Okay, no more guessing... show your work :P

Answer 38

2a+b=1

Answer 39

Show your work... let me know you're not guessing...

Answer 40

(-2)^2+a(-2)-b=3
4-2a-b=3
-2a-b=3-4
-2a-b=-1
-2a-b=-1 divide by -1
2a+b=1

Answer 41

Much better.
Now you have both
a - b = 5 and
2a + b = 1

I can trust you can solve this system with ease now?

Answer 42

2a+b-1=0

Answer 43

We certainly have a lot to work on -.-
FIRST EQUATION
a - b = 5
adding b to both sides gives
a = b + 5

Now substitute b+5 for the a in the SECOND equation:
2(b+5) + b = 1
SOLVE
FOR
b.

Get to it...

Answer 44

a=2
b=-3, correct ba toh??

Answer 45

Nice going, *peanut-butter boy*
:P

Answer 46

da eff???? how da eff,,

Answer 47

pff...
Google Derek Bocar... first result...
You take so long, I have to find ways to ... kill time... and guess what came up? XD

Answer 48

yeah,, that was really long time agoo, T_T

Answer 49

most humiliating scandal

Answer 50

mhmm... last bit just killed my appetite :D

Answer 51

But enough about that.
Job well done... you certainly picked this up with more speed than Faye...

Answer 52

i'm really sleeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeepyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy!!!!!!

Answer 53

Join the club.
Why don't you listen to yourself playing? >:)

Answer 54

LOL Just kidding
Peace ^_^

Answer 55

NOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 56

i'm gonna hack their youtube account!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

Answer 57

*his

Answer 58

Come to think of it... just how good are you with that fiddle?

Answer 59

ahm,, xDDD average?? xDDD not really an expert,

Answer 60

figures... that's no use, I need to hear it.
Any excerpts?

Answer 61

i don't really play classical music, so long,,,, xDDD

Answer 62

nope,, i don't really show my skills too much, xDD

Answer 63

Le gasp... okay, interest over XD

time to play some notes on a keyboard...


...the one that looks like a monster's smile and not the one with QWERTY written on it...

Answer 64

<plays some random stuff>

Answer 65

@derek11111
Listening to myself play is making me even sleepier... you should follow suit.
Good night, -peanut butter boy-

XD
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Terence out
^_^