If x^2 (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

Given that gathered x^3 (2 x-1)(x+2)(x-3) = A+ B 2 x-1 + C x+2 + D x-3 gathered Let aligned f(x) & = x^3 (2 x-1)(x+2)(x-3) & = x^3 (2 x-1) (x^2-x-6 ) & = x^3 2 x^3-3 x^2-11 x+6 aligned Here we see that the power of x will be same in Nr and Dr. First we divide the numerator by denominator array cc & x^3 (2 x-1)(x+2)(x-3) = & 1 2 + 3 2 x^2+ 11 2 x-3 (2 x-1)(x+2)(x-3) & A= 1 2 array