Question

let P(X)= x^4-2x^3+3x^2-ax+b be a polynomial such that when it is divided by x+1 and x-1 and the reminder are 19 and 5 find the remainder when p( x) is divided byx-3

Answer 1

When divided by x+1 :-
1+2+3+a+b=19
a+b=13
When divided by x-1:-
1-2+3-a+b=13
-a+b=11
Solving
2b=24
b=12
a=1
when x =3,remainder=
81-54+27-3+12=63