Question: a. Use synthetic to show that 3 is a solution of the polynomial equation

\[14{{x}^{3}}-17{{x}^{2}}-16x-177=0\]

b. Use the solution form part (a) to solve this problem. The number of eggs, f(x), in a

female moth is a function of her abdominal width, x, in millimeters, modeled by

f(x) = \[\begin{aligned} & 14{{x}^{3}}-17{{x}^{2}}-16x+34. \\ & \\ \end{aligned}\] What is the abdominal width when there are \(211\) eggs?