  We show that given an ideal I generated by regular functions f_1,...,f_r on
the smooth complex variety X, the Bernstein-Sato polynomial of I is equal to
the reduced Bernstein-Sato polynomial of the function g=\sum_{i=1}^rf_iy_i on
the product of X with an r-dimensional affine space. By combining this with
results from [BMS], we relate invariants and properties of I to those of g. We
also use the result on Bernstein-Sato polynomials to show that the Strong
Monodromy Conjecture for Igusa zeta functions of principal ideals implies a
similar statement for arbitrary ideals.
