Finding k so x-2 divides a polynomial in Q[x] and x+1 divides one in Z5[x]

[dash]

1. Polynomial division

a) For what values of k is x-2 a factor x^4 – 5x^3 + 3x + k in Q[x]?

b) For what values of k is x+1 a factor of x^4 + 2x^3 – 3x^2 + kx + 1 in Z5[x]

 

[Hurkyl]

Dash, you need to show what effort you have put into the problem before we can help you. This is both common sense and site policy. Until you are willing to do so, please stop posting your homework questions.

 

[dash]

my problem is that I don't know how to start the problem?

 

[HallsofIvy]

Are you saying you do not know how to divide? "Polynomial division" is basically the same as "long division" in arithmetic: choose a "trial quotient" based on the term with the highest power, multiply by the divisor and subtract from the dividend. Repeat.