Description: Implement a polynomial class using a LinkedList defined in Java (1) Define a polynomial that has the following methods for Polynomial a. public Polynomial() POSTCONDITION: Creates a polynomial represents 0 b. public Polynomial(double a0) POSTCONDITION: Creates a polynomial represents a constant a0 c. public Polynomial(Polynomial p) POSTCONDITION: Creates a polynomial that is the copy of p d. public void add_to_coef(double amount, int exponent) PRECONDITION: amount!=0 POSTCONDITION: Adds the given amount to the coefficient of the specified exponent. Note: the exponent is allowed to be greater than the degree of the polynomial example: if p = x + 1, after p.add_to_coef(1, 2), p = x^2 + x + 1 if p = x + 1, after p.add_to_coef(1.5, 1), p = 2.5x + 1 if p = x + 1, after p.add_to_coef(-1, 1), p = 1 e. public void assign_coef(double coefficient, int exponent) POSTCONDITION: Sets the coefficient for the specified exponent. Note: the exponent is allowed to be greater than the degree of the polynomial the coefficient may be 0 if p = x + 1, after p.assign_coef(1.5, 2), p = 1.5x^2 + x + 1 if p = x + 1, after p.assign_coef(1.5, 1), p = 1.5x + 1 if p = x + 1, after p.assign_coef(0, 1), p = 1 if p = x + 1, after p.assign_coef(0, 0), p = x f. public double coefficient(int exponent) POSTCONDITION: Returns coefficient at specified exponent of this polynomial. Note: the exponent is allowed to be greater than the degree of the polynomial e.g. if p = x^2 + 1; p.coeffcient(3) should return 0, and p.coeffcient(1) should return 0 and p.coeffcient(2) should return 1 g. public double eval(double x) POSTCONDITION: The return value is the value of this polynomial with the given value for the variable x. Use Horner's rule. Try not to use power method from Math, which is very low efficient h. public string toString() POSTCONDITION: return the polynomial as a string like 2x^2 + 3x + 4 i. public Polynomial add(Polynomial p) POSTCONDITION: this object and p are not changed return a polynomial that is the sum of p and this polynomial j. public Polynomial multiply(Polynomial p) POSTCONDITION: this object and p should not be changed returns a new polynomial obtained by multiplying this term and p. For example, if this polynomial is 2x^2 + 3x + 4 and p is 5x^2 - 1x + 7, then at the end of this function, it will return the polynomial 10x^4 + 13x^3 + 31x^2 + 17x + 28. (2)Implementation options. No matter which option you choose, (a) the terms should be stored in decrees orders of the exponents. (b) Except the constant term , all other terms are stored only if the coefficient is non-zero option1 a. Define TermNode as a public class which has i. three instance variables: double coeff int exp Term next; ii. constructor (int exp, double coeff, TermNode nextTerm ) iii. get, set method, and other methods as needed. b. Polynomial has the following instance variables: TermNode first; //first is a reference to the the first term of a linked list of terms, // which are sorted in decresing order of exponent. This makes it easy for the // add, multiply, and toString methods. option2 or a. Define TermNode as a nested static class in Polynomial, which has i. three instance variables: double coeff int exp Term next; ii. constructor (int exp, double coeff, TermNode nextTerm ) b. Polynomial has the following instance variables: TermNode first; //first is a reference to the the first term of a linked list of terms, which are sorted in decresing order of exponent option3 using LinkedList defined in Java a. Define Term as a nested static class in Polynomial, which has i. two instance variables: double coeff int exp ii. constructor (int exp, double coeff) b. Polynomial has the following instance variables: LinkedList first; //first is a reference to the the first term of a linked list of terms, which are sorted in decresing order of exponent