Linear Transformations · Challenge problem

Let $T:\mathcal{P}_3\to\mathbb{R}^4$ be $T(p) = \big(p(0),\ p(1),\ p(2),\ p(3)\big)$, where $\mathcal{P}_3$ is the space of polynomials of degree at most $3$. Find the determinant of the matrix of $T$ with respect to the basis $1, x, x^2, x^3$ of $\mathcal{P}_3$ and the standard basis of $\mathbb{R}^4$.