The degree of a polynomial is determined by the term with the highest exponent. In this case, you have the polynomial \(x^2(2x-3)^2\).
To find the degree, first expand \((2x-3)^2\):
\((2x-3)^2 = (2x-3)(2x-3) = 4x^2 - 12x + 9\)
Now, you have \(x^2(4x^2 - 12x + 9)\).
The highest exponent in this polynomial is 4 (from the \(4x^2\) term), so the degree of the polynomial \(x^2(2x-3)^2\) is 4.