What are the two critical points and three possible intervals for this solution? ,-6,-4) ,-6,0) ,0,-6) ,0,10)

Step-by-step explanation:

In this problem the "critical points" are the x-intercepts.  Find these by setting x^2 + 12x + 35 = to 0 and solving for x.  The coefficients of this quadratic are a = 1, b = 12 and c = 35, and so the discriminant is b^2-4(a)(c) = 144-4(1)(35), or 4.

Thus, the roots (x-intercepts) are:

       -12 ± √4          -12 ± 2         -6 ± 1

x =   = =  =  -5 and -7.

The intervals in question are thus (-infinity, -7), (-7, -5), (5, infinity).  Possible test points (one from each interval) are { -10,  -6,  10}

          2(1)                   2                 1