****NEEDS TO BE IN C++ ********

Implement and test a preliminary version of the polynomial class, using a small array to store the coefficients of the polynomial in order of increasing exponents, following the design pattern of object-oriented approach. Suppose the range of the exponents is in [0, 30).

Use an array as a private member variable.

insert(), adding a new term on specific exponent.

remove(), deleting a term.

Have a add() method, deciding the parameters and the return value by yourself.

Have a sub() method, deciding the parameters and the return value by yourself.

A printout() method to display the polynomial expression.

And other variables, or methods if needed.

Do the algorithm analysis on the implemented method, and give the big O notation estimation.

You will also need to write a PolynomialTest program to initialize two linear polynomial objects and apply the operation on it and also display the result. For example, P1=x + 3x⁵ - 5x⁸; P2= 2x³ - 4x⁵+ 2x⁷; So P3= P1+P2= x +2x³ - x⁵+ 2x⁷ - 5x⁸, P4 = P1-P2 = x - 2x³ + 7x⁵- 2x⁷ - 5x⁸.

In this project, only one variable is considered, we dont have the polynomial such as x+3x⁵ 3y³ .

*****Need to provide:

problem statement, analysis of ALGORITHM COMPLEXITY, algorithm design, program Input/Output, and tested result (analysis your result).

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