Question

If the polynomial (2x2+ax+3x-5) and (x3+x2-4x-a) leave the same remainder when divided by x-1  find the value of a

Answer 1

$Reminder\ of\ 2 x^{2} + (a+3) x - 5 \ \ \ \ \ when\ divided\ by\ x-1 \ is\\\\ 2 * 1^{2} + (a + 3) 1 - 5\\ a\\\\ Reminder\ of\ x^{3} + x^{2} - 4 x - a\ \ when \ divided\ by \ x-1 \ is \\ \\ 1^{3} + 1^{2} - 4 * 1 - a \\ -2 -a \\ hence \ \ \ \ a \ = \ -2 \ - a\\ 2a = -2 \\a = -1$

answer is a = -1