In control system analysis, transfer functions are developed that mathematically relate the dynamics of a system?s input to its output. A transfer function for a robotic positioning system is given by

Where G(s) = system gain, C(s) = system output, N(s) = system input, and s = Laplace transform complex frequency. Use a numerical technique to find the roots of the numerator and denominator and factor these into the form

Where ai and bi = the roots of the numerator and denominator,respectively.

+ 12.5s? +50.5s + 66 C(s) G(s) = N(s) s+ 19s + 122s2 + 296s + 192