For the equation y = a + bx + cx² + dx³ and a list of observations X
and Y it uses a multiple regression:

=LINEST(Y,X^{1,2,3})

To see the result array-enter (with ctrl+shift+enter) in a 4x1 range or
highlight the formula and press F9.

Jon H wrote:

I'm curious as to what methods excel uses when it calculates a polynomial
curve of best fit, i.e. if you graphed two sets of values and added a
trendline in the graph of the polynomial type, how does it determine the
constant coefficients of the function it produces?