find the numerical values of the constants A, B and C such that 2x^3 +7x^2-x-6=(Ax+1)(x-1)(x+B)+4x-C
well, just expand and equate coefficients:
2x^3 +7x^2-x-6 = Ax^3+(AB-A+1)x^2+(B+3-AB)x+(-B-C)
So, you have
A = 2
AB-A+1 = 7
B+3-AB = -1
-B-C = -6
A=2, so you have
2B-2+1=7, so B=4
That better work with
B+3-AB = -1
4+3-2*4 = -1 -- check
-B-C = -6
-4-C = -6
C=2