# APL(NARS), 7 chars
{⍵⊥⌽⍺}∂
For the input of polynom the list
$$ a_0 a_1 ... a_n $$
means polynom
$$ a_0+a_1 X^1+ ... +a_n X^n $$
test:
f←{⍵⊥⌽⍺}∂
4 5 f ¯13
5
0 0 0 4 ¯2 0 0 0 0 0 5 f 19
1.613438484E13
0 0 0 0 0 f 400
0
0 f 400
0
0 0 48 0 4.14 f ¯3
¯735.12
¯5 0 0 1 f 5.4
87.48