+147 Find the greatest integer value of $b$ for which the expression $\frac{9x^3+4x^2+11x+7}{x^2+bx+8}$ has a domain of all real numbers.
+1223 \(x^2 + bx+ 8\) = 0 has to have no real solutions. So, the discriminant neds to be less than 0.
\(\Delta = b^2 - 4ac= b^2 - 32 < 0\)
\(b^2 < 32\)
The greatest integer value of b is 5.
