Find the greatest integer value of b for which the expression (9x^3 + 4x^2 + 11x + 7)/(x^2 + bx + 18) has a domain of all real numbers.
This will have a domain of all real numbers if the discriminant of the quadratic in the denominator is < 0
So
b^2 - 4*18 < 0
b^2 - 72 < 0
b^2 < 72
b = 8
+743 
