Question

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)

Answer 1

love remainder/factor theorem

Answer 2

P(x)=Q(x)D(x)+R

Answer 3

\[\frac{x-1+4}{x-1}\]
\[\frac{x-2+5}{x-2}\]
since f(x) = x+3 is "a" solution .... i wonder if we can be this specific

Answer 4

i think we look more at the remainder theorem here.

Answer 5

For this speicfic question P(x)=Q(x)(x-1)(x-2)+(Ax+B)

Answer 6

The remainder is a linear factor as it is 1 degree lower than a quadratic

Answer 7

Is this guy online?

Answer 8

prolly not .... but the question was nice

Answer 9

Anyway we know P(1)=4 from first lot of info
and P(2)=5

Answer 10

now its just simultaneous equations

Answer 11

So we get

A+B=4
2A+B=5

Answer 12

A=1 B=3

Answer 13

tHEREFORE remainder is x+3

Answer 14

so i was right :)

Answer 15

which is what u got i guess haha

Answer 16

i gotta hand it to you