Hello everyone! Code provided below was given as homework. As you guys can notice there are some constructors and methods that we have to create in order to makes it run well, any help will be welcomed, thanks...

public class X00000000 extends Polynomial { public static void main(String args[]) throws Exception { Polynomial p = new X00000000(" X^5"), q = new X00000000("X^2 - X + 1"); Utility.run(p, q); } public X00000000(String s) { // complete this code } public X00000000() { super(); } public Polynomial add(Polynomial p) { Polynomial ans = new X00000000(); // complete this code return ans; } public Polynomial subtract(Polynomial p) { Polynomial ans = new X00000000(); // complete this code return ans; } public Polynomial multiply(Polynomial p) { Polynomial ans = new X00000000(); // complete this code return ans; } public Polynomial divide(Polynomial p) throws Exception { Polynomial ans = new X00000000(); // complete this code return ans; } public Polynomial remainder(Polynomial p) throws Exception { Polynomial ans = new X00000000(); // complete this code return ans; } } //------- cut here. Place your new code above this line and submit only the ------ //------- code above this line as your homework. Do not make any code changes ---- //------- below this line. --------- abstract class Polynomial { DList data = null; public Polynomial() { data = new DList<>(); } public final String toString() { String ans = ""; boolean starting = true; try { DNode n = data.getFirst(); while (n != null) { if (!starting && n.getData().isPositive()) ans += " +"; starting = false; ans += " " + n.getData().toString(); n = data.getNext(n); } } catch (Exception e) { if (starting) return "0"; } return ans; } abstract public Polynomial add(Polynomial p); abstract public Polynomial subtract(Polynomial p); abstract public Polynomial multiply(Polynomial p); abstract public Polynomial divide(Polynomial p) throws Exception; abstract public Polynomial remainder(Polynomial p) throws Exception; } class Utility { public static void run(Polynomial p, Polynomial q) throws Exception { System.out.println("Polynomials p = " + p + " q = " + q); System.out.println("Sum " + p.add(q)); System.out.println("Difference " + p.subtract(q)); System.out.println("Product " + p.multiply(q)); System.out.println("Quotient " + p.divide(q)); System.out.println("Remainder " + p.remainder(q)); } } class Term { Double coefficient; int degree; public Term() { this(null, 0); } public boolean isPositive() { return coefficient > 0; } public Term(Double coefficient, int degree) { this.coefficient = coefficient; this.degree = degree; } public Double getCoefficient() { return coefficient; } public void setCoefficient(Double coefficient) { this.coefficient = coefficient; } public int getDegree() { return degree; } public void setDegree(int degree) { this.degree = degree; } public String toString() { String ans = ""; if (coefficient.doubleValue() == 0) return ""; if (degree == 0) return coefficient.toString(); if (coefficient != 1) { if (coefficient == -1) ans += "-"; else ans += coefficient + " "; } ans = ans + "X"; if (degree == 1) return ans; return ans + "^" + degree; } } class DList { private DNode header, trailer; private int size; public DList() { size = 0; header = new DNode(null, null, null); trailer = new DNode(null, header, null); header.setNext(trailer); } // utility methods public int size() { return size; } public boolean isEmpty() { return size == 0; } // give clients access to nodes, but not to the header or trailer public DNode getFirst() throws Exception { if (isEmpty()) throw new Exception("Empty"); return header.getNext(); } public DNode getLast() throws Exception { if (isEmpty()) throw new Exception("Empty"); return trailer.getPrev(); } public DNode getNext(DNode v) throws Exception { DNode ans = v.getNext(); if (ans == null || ans == trailer) throw new Exception("No such node"); return ans; } public DNode getPrev(DNode v) throws Exception { DNode ans = v.getPrev(); if (ans == null || ans == header) throw new Exception("No such node"); return ans; } // methods to change the list public void addBefore(T d, DNode v) { DNode u = v.getPrev(); DNode x = new DNode(d, u, v); u.setNext(x); v.setPrev(x); size++; } public void addAfter(T d, DNode v) { DNode w = v.getNext(); DNode x = new DNode(d, v, w); v.setNext(x); w.setPrev(x); size++; } public void addFirst(T d) { addAfter(d, header); } public void addLast(T d) { addBefore(d, trailer); } public T remove(DNode v) throws Exception { if (v == header || v == trailer) throw new Exception("Sentinel"); DNode u = v.getPrev(); DNode w = v.getNext(); w.setPrev(u); u.setNext(w); size--; return v.getData(); } // LinkedList testing methods: public String toString() { String ans = ""; DNode n = header; ans += "(H)<-->"; do { n = n.getNext(); if (n == trailer) ans += "(T)"; else ans += (n.getData() + "<-->"); } while (n != trailer); return ans; } } class DNode { private T data; private DNode prev, next; public DNode(T d, DNode p, DNode n) { data = d; next = n; prev = p; } public T getData() { return data; } public DNode getNext() { return next; } public DNode getPrev() { return prev; } public void setData(T d) { data = d; } public void setNext(DNode n) { next = n; } public void setPrev(DNode p) { prev = p; } }