You should try dividing P(x) by (x-m)^2 and note that your remainder must be 0. Once you have done this you will end up with a quadratic which you can find the roots for using the standard result.
The polynomial P(x) =x4-4x3+hx2-6x+2 has a factor in the form (x-m)2, find the values of m and h.
P(m) = 0
Try m=1, (1)4-2(1)3+3(1)-2=0
Hence, m=1, h=7
I think there is something wrong in my solution, can anyone help?