Question 1009738

If I have the quadratic function, f(x)= (x^2)-x-12, and I want to find the x-intercept, I have to set y = 0, and factor like so: 0 = (x-4)(x+3).

The questions is: why can't I complete the square or factor like so: 0 = x(x-1)-12 (which leads to 0 = (x-1)(x-12))?  Doing either of those alternative techniques results in different x-intercepts.
<pre>You can use the "complete the square" method to solve for the x-intercepts/solutions to the equation/roots.
However, factoring {{{f(x) = x^2 - x - 12}}} CANNOT be done the following way you proposed: 
{{{f(x) = x^2 - x - 12}}}
{{{0 = x(x - 1) - 12}}}
From this, you CANNOT obtain x - 1 and x - 12 as factors. That's not the proper way to factor a trinomial in
order to find its roots. The 1<sup>st</sup> method: {{{0 = (x - 4)(x + 3)}}}, though is indeed correct.