The polynomial P(x) =x^{4}-4x^{3}+hx^{2}-6x+2 has a factor in the form (x-m)^{2}, find the values of m and h.

P(x) =x^{4}-4x^{3}+hx^{2}-6x+2

P(m) = 0

m^{4}-4m^{3}+hm^{2}-6m+2=0

P’(x) =4x^{3}-12x^{2}+2hx-6

P’(m)=4m^{3}-12m^{2}+2hm-6=0

-m^{5}+4m^{4}+6m^{2}-2m=-2m^{5}+6m^{4}+3m^{2}

m^{5}-2m^{4}+3m^{2}-2m=0

÷m, m^{4}-2m^{3}+3m-2=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?