Extract the common factor: given x * x-5x + 1 = 0, find x * x * x-4x * x-4x-1

Extract the common factor: given x * x-5x + 1 = 0, find x * x * x-4x * x-4x-1

That is X & # 178; - 5x = - 1
So the original formula = x & # 179; - 5x & # 178; + X & # 178; - 5x + X-1
=x(x²-5x)+(x²-5x)+x-1
=-x-1+x-1
=-2

Why is the greatest common factor of F (x) = x ^ 4 + x ^ 3-3x ^ 2-4x-1 and G (x) = x ^ 3 + x ^ 2-x-1 x + 1

f(x)=x^4+x^3-3x^2-4x-1=(x+1)(x^3-3x-1)
g(x)=x^3+x^2-x-1=(x-1)(x+1)^2
The greatest common factor of F (x) and G (x) is x + 1

It is known that the quadratic equation T2 + (2 + I) t + 2XY + (X-Y) I = 0 (x, y ∈ R) with respect to T. when the equation has real roots, then the trajectory equation of point (x, y) is______ ．

Let the real root be t, then T2 + 2T + 2XY + (T + X-Y) I = 0 is obtained from T2 + (2 + I) t + 2XY + (X-Y) I = 0, that is, T2 + 2T + 2XY = 0t + X − y = 0, and (x-1) 2 + (y + 1) 2 = 2 is obtained by eliminating the parameter t, so the answer is: (x-1) 2 + (y + 1) 2 = 2