2023/001) When dividing a polynomial f(x) by $(x-1)^2$ the remainder is x+1. If f(x) is divided by $x^2$ the remainder is 2x+3 . if the remainder when divided by $x^2(x-1)$ is $ax^2+bx+c$ then find a+b+c

 Dividing a polynomial f(x) by $(x-1)^2$ the remainder is $g(x) = x+1$-

so dividing by (x-1) the remainder is $g(1) = 1 + 1 = 2$

Dividing by $x^2(x-1) $ is $ax^2+bx+c$

so deviding  $ax^2+bx+c$ by $x-1$ remainder must be 2

so $f(1) = a + b+ c = 2$