Originally Posted by

**B9766** This is a "why" question. For my example I will use:

$ x^2-4x-5$

Where we are trying to determine the values of x for which the polynomial is entirely positive and those for which it is entirely negative.

I understand that this equation describes a parabola that intersects the x-axis at (-1, 5). I can graph the curve and determine the answers to the question: The curve is positive for $(-\infty,-1)\cup(5,\infty)$

and negative for $(-1,5)$ I could also have tested interval values (as the textbook suggests) to arrive at the same conclusion.

However, I'm interested in the following algebraic logic:

$x^2\ -\ 4x\ -\ 5\ =\ (x-5)(x+1)$

Therefore, for positive parts of the curve, why can't we say:

$(x-5)(x+1) > 0$ therefore $(x-5)>0$, and $(x+1)>0$, therefore $x>5$ and $x>-1$?