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when a polynomial f(x)divided by (x-1)it gives remainder 4 &when divided by (x-2) remainder=5 what will be remainder if f(x)is dividedby (x-1)(x-2)

Mathematics
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love remainder/factor theorem
P(x)=Q(x)D(x)+R
\[\frac{x-1+4}{x-1}\] \[\frac{x-2+5}{x-2}\] since f(x) = x+3 is "a" solution .... i wonder if we can be this specific

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Other answers:

i think we look more at the remainder theorem here.
For this speicfic question P(x)=Q(x)(x-1)(x-2)+(Ax+B)
The remainder is a linear factor as it is 1 degree lower than a quadratic
Is this guy online?
prolly not .... but the question was nice
Anyway we know P(1)=4 from first lot of info and P(2)=5
now its just simultaneous equations
So we get A+B=4 2A+B=5
A=1 B=3
tHEREFORE remainder is x+3
so i was right :)
which is what u got i guess haha
i gotta hand it to you

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