Recall that if ax^2 + bx + c = 0 has solutions x = x1 and x = x2, then a(x - x1)(x - x2) = 0. So...

Recall that if ax^2 + bx + c = 0 has solutions x = x1 and x = x2, then a(x - x1)(x - x2) = 0. So the expression x^2 - x - 1 is equivalent to

(x-((1-√5)/2) (x-((1+√5)/2)
(x-((1+√5)/2) (x-((-1-√5)/2)
(x - 1)(x - 1)
(x - 1)(x + 1)

(x-((1-√5)/2) (x-((1+√5)/2).