For real , let x+k (x-1)(x+2)(x+4) = A x-1 + B x+2 + C x+4 , where , and are…

MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

For real

k

, let

\frac{x+k}{(x-1)(x+2)(x+4)}=\frac{A}{x-1}+\frac{B}{x+2}+\frac{C}{x+4},

where

A

B

and

C

are constants. (i) If

A=2

, find the value of

k

. (ii) Using this value of

k

, determine

B

and

C