Question

The polynomial p(x) =x power 4 -2x power 3 +3x power 2 -ax+b when divided by (x-1)and (x+1) leaves the remainders 5 and 19 respectively. find the values of a and b

Answer 1

In case 1 Put x-1 = 0 to get the value of and substitute it in p(x) 
Similarly do it in case 2 
you will get 2 equations in a and b
eq 1 is b - a = 3
eq 2 is b + a = 13
Add the two equations 
you will get 2b = 16 

Hence B = 8
            A = 5