If x^4 (x-1)(x-2)(x-3) =x+k+ A x-1 + B x-2 + C x-3 , then k+A-B+C=

Step-by-step solution

Given, aligned & x^4 (x-1)(x-2)(x-3) & =x+k+ A x-1 + B x-2 + C x-3 & x^4=x(x-1)(x-2)(x-3)+k(x-1) aligned array r (x-2)(x-3)+A(x-2)(x-3)+B(x-3) (x-1)+C(x-1)(x-2) array on putting x=1 , we get A= 1 2 on putting x=2 , we get B= 16 -1 =-16 on putting x=3 , we get C= 81 2 on putting x=0 , we get aligned 0= & k(-1)(-2)(-3)+ 1 2 (-2)(-3)-16 6 k & =3-48+81=36 k & =6 k+A-B+C & =6+ 1 2 +16+ 81 2 & =6+16+41=63 aligned