think about the graph of the quadratic (a parabola) which opens upward for each of your examples ...

y = x(x-1) crosses the x-axis at x = 0 and x = 1 ... y > 0 when x < 0 and when x > 1

y = 4x^2 + 10x + 6 = 2(2x^2 + 5x + 3) = 2(2x + 3)(x + 1) crosses the x-axis at x = -3/2 and x = -1 ... y < 0 for -3/2 < x < -1

x^2 + 2x + 4 = (x^2 + 2x + 1) + 3 = (x + 1)^2 + 3 > 0 for all x