## smileahuja 2 years ago 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)

• This Question is Open
1. chris00

love remainder/factor theorem

2. chris00

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

3. amistre64

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

4. chris00

i think we look more at the remainder theorem here.

5. chris00

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

6. chris00

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

7. chris00

Is this guy online?

8. amistre64

prolly not .... but the question was nice

9. chris00

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

10. chris00

now its just simultaneous equations

11. chris00

So we get A+B=4 2A+B=5

12. chris00

A=1 B=3

13. chris00

tHEREFORE remainder is x+3

14. amistre64

so i was right :)

15. chris00

which is what u got i guess haha

16. chris00

i gotta hand it to you