1.) x^3 - 6x + x^2 - 6 = 0
x^2(x - 6) + 1(x - 6) = 0
(x - 6)(x^2 + 1) = 0
x - 6 = 0 or x^2 + 1 = 0
x = 6 x^2 = -1
x = ±i
2.) x^2 + 5x + 6 is greater than or equal to 0
(x + 2)(x + 3) ? 0
x ? -3 or x ? -2
3.) f(x) = -x^2 + 2x + 3
This function has a parabolic graph, with vertex (1, 4), opening downward, with x-intercepts -1 and 3.
4.) f(x) = x^2 + 5x + 4
This function has a parabolic graph, with vertex (-5/2, -9/4), opening upward, with x-intercepts -1 and -4.
5.) f(x) = -6x^2 - 12x - 5
This function has a parabolic graph, with vertex (-1, 1), opening downward. Its x-intercepts have irrational coordinates.
6.) x^2 + 6x = x(x + 6)
If this were an equation, its solutions would be 0 and -6.