Polynomial Problems in Java

You will 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 don’t have the polynomial such as x+3x⁵ 3y³ .

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public class Polynomial {
    private int [] terms;   
   
    /**
    * constructor
    * Suppose the range of the exponents is in [0, 30).
    */
    public Polynomial() {
       terms = new int[30];      
       for (int i = 0; i < terms.length; i++) {
            terms[i] = 0;
       }
    }
   
    /**
    * adding a new term on specific exponent.
    * @param term
    * @param exponent
    */
public void insert(int term, int exponent){
       if (exponent < 0 || exponent >= 30) {
            throw new ArrayIndexOutOfBoundsException("exponent must be a positive number and less tahn 30");
       }
       terms[exponent] = term;      
    }...