If x 2 + 5 x + 7 ( x - 3 ) 3 = A ( x - 3 ) + B ( x - 3 ) 2 + C ( x - 3 ) 3 , then 9 A - 3 B + C =

Step-by-step solution

Given, x 2 + 5 x + 7 ( x - 3 ) 3 = A ( x - 3 ) + B ( x - 3 ) 2 + C ( x - 3 ) 3 x 2 + 5 x + 7 ( x - 3 ) 3 = A ( x - 3 ) 2 + B ( x - 3 ) + C ( x - 3 ) 2 x 2 + 5 x + 7 = A ( x - 3 ) 2 + B ( x - 3 ) + C Put x = 3 9 + 15 + 7 = A ( 0 ) + B ( 0 ) + C ⇒ c = 31 x 2 + 5 x + 7 = A ( x 2 - 6 x + 4 ) + B ( x - 3 ) + C x 2 + 5 x + 7 = A x 2 + ( B - 6 ) x + 9 A - 3 B + C Comparing x 1 ,   x 2 coefficients & constant coefficients A = 1 ,   B - 6 = 5                   &#1