Q$2$ Consider a polynomial in two variables $x$ and $y$ :

$p(x,y)={\displaystyle \underset{i=0}{\overset{d_x}{}}}{\displaystyle \underset{j=0}{\overset{d_y}{}}}{a}_{i,j}{x}^i{y}^j$

where $d_x$ and $d_y$ are the highest degrees of $x$ and $y$ respectively, and $a_{i,j}$

is the coefficient of $x^i{y}^j.$

Suppose $d_x{d}_y$ :

Devise an "efficient" algorithm to evaluate polynomials of the above

form.

$[1$ point$]$

What is the time complexity of your algorithm? Justify your answer.

$[1$ point$]$