Estimating the complexity by the calculation of the number of real multiplications in a general polynomial function
The direct computation should be straightforward. Since I suspect the exercice has other purposes (more advanced algorithmic complexity), there additionally are a couple of tricks to reduce the complexity of power evaluations.

First, if you have to evaluate all powers $y^0,y^1,\,\cdots,y^Q$, you can store the power-of-two powers, and use the binary expansion of a power $q$. It can be called exponentiation by squaring. For instance, to compute $y^7$, you need one multiply for $y^2 = y\times y$, one for  $y^4=y^2\times y^2$ and two more for $y \times y^2 \times y^4$, so four multiplies instead of six by direct computation. And the $y^2$ and $y^4$  can be stored for the next powers.

Second, a classical polynomial evaluation is "Horner's scheme": 

$$a_0 x^n + a_1 x^{n-1} + \cdots + a_n =  \left(\left(\left( a_0x+a_1\right) x \right)\ldots a_{n-1}\right)x+ a_n$$
which can be adapted to your case.