If x^3 (2 x-1)(x+2)(x-3) =A+ B 2 x-1 + C x+2 + D x-3 , then A is equal to

Step-by-step solution

aligned & x^3 (2 x-1)(x+2)(x-3) = A 1 & + B 2 x-1 + C x+2 + D x-3 aligned aligned & A(2 x-1)(x+2)(x-3)+B(x+2)(x-3) & = +C(x-3)(2 x-1)+D(2 x-1)(x+2) (2 x-1)(x+2)(x-3) & aligned gathered A(2 x-1)(x+2)(x-3)+B(x+2) (x-3)+C(x-3)(2 x-1)+D(2 x-1) (x+2)=x^3 gathered Put x=3 , we obtain D(5)(5)=27 D=27 / 25 Put x=-2 , we obtain C(-5)(-5)=-8 C=-8 / 25 Put x= 1 2 , we obtain B(5 / 2)(-5 / 2)=1 / 8 B=-1 / 50 Put x=0 , we obtain array r A(-1)(2)(-3)+ (- 1 50 )(2)(-3)+ (- 8 25 )(-3)(-1)+ 27 25 (-1)(2)=0 6 A+ 3 25 - 24 25 - 54 25