Solve each inequality
1.x^2+12x+39>12
x^2+12x+39>12
x^2 + 12x + 27 > 0
(x+9)(x+3) > 0
To be > 0, both factors must be either positive or both negative
x+9>0 AND x+3> 0 --- OR --- x+9<0 AND x+3<0
x > -9 and x > -3 --- OR --- x < -9 and x < -3
x > -3 --- OR --- x < -9
another approach:
consider the function y = x^2 + 12x + 27
where is the parabola above the x-axis, that is, where is y > 0 ?
factor and solve as above
the x-intercepts are -3 and -9
so solution: x < -9 OR x > -3