If ( 8 (x+3)^2(x-2) = A x+B (x+3)^2 + C x-2 ), then (25(B+8 C-A)= )

Step-by-step solution

Given, ( aligned & 8 (x+3)^2(x-2) = A x+B (x+3)^2 + C x-2 & 8 (x+3)^2(x-2) = (A x+B)(x-2)+C(x+3)^2 (x+3)^2(x-4) & 8=(A x+B)(x-2)+C(x+3)^2 & At x=2 & 8=0+C(5)^2 & 8=25 C C= 8 25 & At x=0 , & 8=(B)(-2)+C(9) & 8=-2 B+9 C & 8=-2 B+ 72 25 ( C= 8 25 ) & 2 B= 72 25 -8 & 2 B= 72-200 25 = -128 25 & B= -64 25 & At x=1 , & 8=(A+B)(-1)+C(4)^2 & 8=-A-B+16 C & 8=-A+ 64 25 + 128 25 & A= 192 25 -8 A= -8 25 aligned ) Now, (25(B+8 C-A)=25 ( -64 25 + 64 25 + 8 25 ) ) (=25 8 25 =8 )