jakub -- Sage

expand((x^2-2*x+5)*(x-2)^2*(x-3))

x^5 - 9*x^4 + 35*x^3 - 79*x^2 + 104*x - 60

x^5 - 9*x^4 + 35*x^3 - 79*x^2 + 104*x - 60

M=Matrix([[1,0,3,-1],[-1,1,-1,-1],[0,-1,0,3],[1,0,1,0]]); A=M.inverse(); M*A

[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]

[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]

expand((x+13)*(x-39/4)*(x-13/4))

x^3 - 2197/16*x + 6591/16

x^3 - 2197/16*x + 6591/16

3*(-2197/16)+(6591/16)

solve(x^4-3*x^3-13*x^2+27*x+36,x)

[x == -3, x == -1, x == 3, x == 4]

[x == -3, x == -1, x == 3, x == 4]

p(x)=x^4-3*x^3-13*x^2+27*x+36; p(0); p(1); p(2)

36
48
30

36
48
30

var('a'); M=Matrix([[2,2,2,-a],[2,2,-a,2],[2,-a,2,2],[-a,2,2,2]]); solve(det(M),a)

[a == 6, a == -2]

[a == 6, a == -2]

jakub