Answer 1

Leftf(x)=`x^3+ax^2+bx+6`   

`x-2=0`⇒ x=2

Since, x-2 is a factor, remainder=0 

∴ f(2)=0  

`(2)3+a(2)^2+b(2)+6=0`  

`8+4a+2b+6=0`   

`2a+b+7=0`  .........(1) 

On dividing f(x)by x-3, it leavvves a  remainder 3. 

∴ f(3)=3 

`(3)^3+a(3)^2+b(3)+6=3` 

`27+9a+3b+6=3` 

`3a+b+10`  ...........(2)

Subtracting (1) from (2), we get,  

a+3=0   

a=-3 

Substituting the value of a in (1), we get, 

-6+b+7=0 

b=-1