Diving into Scala's Parsing Combinators

Given an algebraic expression, reduce the expression to a simplified form meeting the following criteria:

• All terms are in descending order of the power of variable x.

• Coefficients should be concatenated immediately to the left of your variable (e.g.: 5 * x should be printed as 5x).

• There are exactly 3 characters between any 2 consecutive terms of the expression: a space, followed by a + or - sign, followed by another space.

• In case there is no operator between expressions, assume that it implies multiplication. e.g. (5x+2)(x+2) should be treated as (5x+2)*(x+2), 5(x+1) should be treated as 5*(x+1).

• The simplified expression must not contain any parentheses.

• 1-coefficients and 1-powers are implied; if the coefficient or power of a certain x term is 1, do not output 1 (e.g.: 1x or 1 * x simplifies to x, and x^1 simplifies to x).

• Do not print the powers of x having a coefficient of 0 (e.g.: output 5x^2 - 3, not 5x^2 + 0x - 3).

The original challenge comes from HackerRank