The polynomial p(x)=x4−2x3+3x2−ax+b when divided by (x-1) and (x +1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when p(x) is divided by (x -2).

The polynomial p(x)=x4−2x3+3x2−ax+b when divided by (x-1) and (x +

1.	The polynomial p(x)=x4−2x3+3x2−ax+b when divided by (x-1) and (x +1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when p(x) is divided by (x -2).
Answer» The polynomial $p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + b$ when divided by (x-1) and (x +1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when p(x) is divided by (x -2).