Edit: Should of course be without plusses in the matrix form:

    [x1^3, x1^2, x1, 1] [a] = [y1]
    [x2^3, x2^2, x2, 1] [b] = [y2]
    [x3^3, x3^2, x3, 1] [c] = [y3]
    [x4^3, x4^2, x4, 1] [d] = [y4]