Question

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

Answer 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