Pretty Print Polynomials
Retina 0.8.2, 56 bytes

(?=( \S+)+)
x^$#1
\b0x.\d+&#32;

\b1x
x
x.1&#32;
x&#32;
 0

 -
-
&#32;
+


Try it online! Link includes test cases. Explanation:

(?=( \S+)+)
x^$#1


Insert all of the powers of x, including x^1 but not x^0.

\b0x.\d+ 


Delete all powers of x with zero coefficients, but not a trailing 0 (yet).

\b1x
x


Delete a multiplier of 1 (but not a constant 1).

x.1 
x 


Delete the ^1 of x^1.

 0



Delete a constant 0 unless it is the only thing left.

 -
-


Delete the space before a -.

&#32;
+


Change any remaining spaces to +s.