Find the value of k so that the remainder is - 12 for (2x^4 + 4x^3-7x^2 - kx + 9) / (x-1).

First of all let x-1=0

x=1

Therefore,

P (x) = 2x^4+4x^3-7x^2-kx+9

P (1) = 2 (1) ^4+4 (1) ^3-7 (1) ^2-k (1) + 9

2 (1) + 4 (1) - 7 (1) - k+9=0

2+4-7-k+9=0

15-7-k=0

8-k=0

-k=-8

Therefore, k=8