Design a Read Only Memory $($ROM$)$ to implement the following polynomial

$A=3(2x^2+1),$ with input $(x)$:$,0(x)7$

$($a$)$ What is the size of the initial $($unsimplified$)$ ROM $?$

$($b$)$ What is the size of the final $($simplified$)$ ROM $?$

$($c$)$ Show in detail the final ROM layout, using LogiSim.