maths remainder theorem?

1.When kx^3+x^2-x-3 is divided by x+2,the
remainder is 5.Find the value of k.

set f(x)= kx^3+x^2-x-3
5=f(-2)=-8k+4+2-3 ---> k= -1/4 ...Ans


2.When x^3-x^2+3x+k is divided by x-4,the
remainder is -8.Find the value of k.

set f(x)= x^3-x^2+3x+k
-8=f(4)=64-16+12+k ---> k= - 68 ...Ans

3.When x^3+kx^2+kx+5 is divided by 4x+3,the remainder is 11.Find the value of k.

set f(x)=x^3+kx^2+kx+5
11=f(-3/4)= - 27/64 + 9k/16 - 3k/4 + 5 ---> k= -137/4 ...Ans

4.When 2x^3-2x^2-kx-5k is divided by 2x-1,the remainder is 15.Find the value of k.

set f(x)= 2x^3-2x^2-kx-5k
15=f(1/2)=1/4-1/2-k/2-5k ---> k= - 61/22 ...Ans