Find the values of A. B and C if the expression Ax(x-2)(x+3)+Bx(x-2)+Cx(x+3)+(x-2)(x+3) has a constant value for all values of x
let that constant value be k
according to your wording , we should get a value of k no matter what x we choose.
let x = 0
then 0A + 0B + 0C + (-2)(3) = k
k = -6
let x = 2, 0 + 0 + 10C + 0 = -6
C = -3/5
let x = -3 , 0 + 15B + 0 + 0 = -6
B = -2/5
let x = -1 , 6A + 3B - 2C -6 = -6
6A + 3B - 2C = 0
6A - 6/5 + 6/5 = 0
A = 0
A = 0 , B = -2/5 , C = -3/5
testing for x = 7
0- (2/5)(7)(5) - (3/5)(7)(10) + 5(10)
= 0 - 14 - 42 + 50 = -6
check my arithmetic