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.

- anonymous

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- terenzreignz

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)

- anonymous

x-c

- terenzreignz

wth?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

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

- terenzreignz

mhmm
so
p(1) = ?

- anonymous

i was just asking what x-c is.

- terenzreignz

Just an example.

- anonymous

oh. xDD

- terenzreignz

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

- terenzreignz

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

- anonymous

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

- anonymous

after that??

- terenzreignz

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

- anonymous

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

- terenzreignz

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

- terenzreignz

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

- terenzreignz

... stay with me here...

- anonymous

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

- terenzreignz

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

- anonymous

ahah, xDD sorry,, didn't see thatxDD

- anonymous

after that??

- terenzreignz

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.

- terenzreignz

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

- anonymous

huh??

- anonymous

sorry,, we just started doing that today, xDD

- terenzreignz

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

- anonymous

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

- terenzreignz

simplify...

- anonymous

4-2a-b

- terenzreignz

And this is equal to...?

- anonymous

2a-b=-4

- terenzreignz

Excuse me...?

- anonymous

my eyes hurts,.. T_T

- terenzreignz

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

- anonymous

-2a-b=4

- terenzreignz

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

- terenzreignz

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

- anonymous

2a+b=1

- terenzreignz

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

- anonymous

(-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

- terenzreignz

Much better.
Now you have both
a - b = 5 and
2a + b = 1
I can trust you can solve this system with ease now?

- anonymous

2a+b-1=0

- terenzreignz

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...

- anonymous

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

- terenzreignz

Nice going, *peanut-butter boy*
:P

- anonymous

da eff???? how da eff,,

- terenzreignz

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

- anonymous

yeah,, that was really long time agoo, T_T

- anonymous

most humiliating scandal

- terenzreignz

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

- terenzreignz

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

- anonymous

i'm really sleeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeepyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy!!!!!!

- terenzreignz

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

- terenzreignz

LOL Just kidding
Peace ^_^

- anonymous

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

- anonymous

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

- anonymous

*his

- terenzreignz

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

- anonymous

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

- terenzreignz

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

- anonymous

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

- anonymous

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

- terenzreignz

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...

- terenzreignz

- terenzreignz

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.