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).
Now,When px is divided by x-1, the remainder is p1.When px is divided by x+1, the remainder is p-1.
Thus, we have:
Adding (1) and (2), we get:
By putting the value of b, we get the value of a, i.e., 5.
∴ a = 5 and b = 8
When px is divided by x-2, the remainder is p(2).
Thus we have: