We are given a polynomial with the following structure

$P(x)=(a_0+a_{1}x+a_2{x}^2{)}^2(b_0+b_{1}x{)}^4(c_0+c_{1}x+c_2{x}^2{)}^8$

where $a_0,a_1,a_2,b_0,b_1,c_0,c_1,$ and $c_2$ are arbitrarily given coefficients. What is the minimum number of multiplications do you need to find the value of $P(x)$ for any value of $x?$