  The $K$-theory of a polynomial ring $R[t]$ contains the $K$-theory of $R$ as
a summand. For $R$ commutative and containing $\Q$, we describe
$K_*(R[t])/K_*(R)$ in terms of Hochschild homology and the cohomology of
K\"ahler differentials for the $cdh$ topology. We use this to address Bass'
question, on whether $K_n(R)=K_n(R[t])$ implies $K_n(R)=K_n(R[t_1,t_2])$. The
answer is positive over fields of infinite transcendence degree; the companion
paper arXiv:1004.3829 provides a counterexample over a number field.
