## Master.RohanChakraborty 3 years ago \[ Using \ factor \ theorem,\ prove \ that \a + b, \ b + c \ and \ c + a \ are \ the \\ factors \ of \ (a+b+c)^3 - (a^3 + b^3 + c^3)\] 2. If f(x) = x4 - 2x3 + 3x2 - ax + b is a polynomial such that when it is divided by x - 1 and x + 1, the remainder are 5 and 19 respectively. Determine the remainder when f(x) is divided by x - 2.

1. Master.RohanChakraborty

@lgbasallote @Rohangrr @Ruchi. @FoolAroundMath

2. Master.RohanChakraborty

3. Master.RohanChakraborty

@nbouscal @No-data Plzzz help

4. Master.RohanChakraborty

@Hero

5. Master.RohanChakraborty

@hamza_b23

6. Master.RohanChakraborty

7. Ruchi.

sorry maths is nt my subject.

8. Master.RohanChakraborty

@Hero can u help

9. Hero

Maybe

10. Master.RohanChakraborty

plzz

11. Hero

Give me 20 minutes

12. Master.RohanChakraborty

Order passed

13. Master.RohanChakraborty

\[ Using \ factor \ theorem,\ prove \ that \ a + b, \ b + c \ and \ c + a \ are \ the \\ factors \ of \ (a+b+c)^3 - (a^3 + b^3 + c^3)\]

14. Master.RohanChakraborty

Perfect Question @Hero 15 mins left

15. Master.RohanChakraborty

16. Hero

By the way, what are you the master of?

17. A.Avinash_Goutham

consider it to be a function of a....say f(a) and now if a+b i s a factor f(-b) =0

18. mukushla

for second part of problem: f(x) is divided by x - 1 the remainder is 5 -----> f(1)=5 (I) f(x) is divided by x + 1 the remainder is 19 -----> f(-1)=19 (II) equations (I) and (II) will give u the unknowns a and b now if f(x) is divided by x - 2 the remainder is f(2)

19. mukushla

first part of question : i go with @A.Avinash_Goutham