  The additive primitive length of an element $f$ of a relatively free algebra
$F_d$ in a variety of algebras is equal to the minimal number $\ell$ such that
$f$ can be presented as a sum of $\ell$ primitive elements. We give an upper
bound for the additive primitive length of the elements in the $d$-generated
polynomial algebra over a field of characteristic 0, $d>1$. The bound depends
on $d$ and on the degree of the element.
  We show that if the field has more than two elements, then the additive
primitive length in free $d$-generated nilpotent-by-abelian Lie algebras is
bounded by 5 for $d=3$ and by 6 for $d>3$. If the field has two elements only,
then our bound are 6 for $d=3$ and 7 for $d>3$. This generalizes a recent
result of Ela Ayd{\i}n for two-generated free metabelian Lie algebras.
  In all cases considered in the paper the presentation of the elements as sums
of primitive can be found effectively in polynomial time.
