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Mathematics
OpenStudy (anonymous):

The polynomial f(x)=x^3+3x^2+ax+b leaves the same remainder when divided by (x-2) as when divided by (x+1). Find the value of a

OpenStudy (anonymous):

I'm working on this.

OpenStudy (anonymous):

how? did you take the two remainders adn make them equal

myininaya (myininaya):

i got a different a

myininaya (myininaya):

let me check what i did

OpenStudy (anonymous):

Yes, you're right myininaya, I made a mistake.

myininaya (myininaya):

a=-23/3 ?

myininaya (myininaya):

oops i made a mistake too lol

OpenStudy (anonymous):

What I did was set the two equal to 0. So, x-2=0 and, x+1=0 I got 2 and -1 Then plug them both into the f(x) 8+12+2a+b=-1+3-a+b Then simplify. 20+2a=2-a 3a=-18 a=-18/3 a=-6

myininaya (myininaya):

yes a=-6 is right! :)

myininaya (myininaya):

myininaya (myininaya):

it doesn't matter what b is

myininaya (myininaya):

b can be any real number

OpenStudy (anonymous):

replace x by 2, replace x by -1, set the results =, solve for a and b right?

myininaya (myininaya):

yep you can do it that way too

OpenStudy (anonymous):

\[-1+3-a+b=8+12+2a+b\]

OpenStudy (anonymous):

\[2-a=20+2a\]\[-18=3a\]\[a=-6\]

OpenStudy (anonymous):

Thank you both

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