jmc

Question

Find constants A, B, and C so that x^2 - 7(x - 2)(x - 3)(x - 5) = Ax - 2 + Bx - 3 + Cx - 5.Enter the ordered triple (A,B,C).

Accepted Answer

Multiplying both sides by (x - 2)(x - 3)(x - 5), we get x^2 - 7 = A(x - 3)(x - 5) + B(x - 2)(x - 5) + C(x - 2)(x - 3).Setting x = 2, we get 3A = -3, so A = -1. Setting x = 3, we get -2B = 2, so B = -1. Setting x = 5, we get 6C = 18, so C = 3. Thus, (A,B,C) = (-1,-1,3).