AMC 12 2024a Problem 15

The roots of $x^3 + 2x^2 - x + 3$ are $p, q,$ and $r.$ What is the value of $$(p^2 + 4)(q^2 + 4)(r^2 + 4)?$$ $\textbf{(A) } 64 \textbf{(B) } 75 \textbf{(C) } 100 \textbf{(D) } 125 \textbf{(E) } 144$