Download the attachedÂ polynomial_project.zipÂ file to your computer. DO NOT unzip it. Instead, follow the instructions on the Eclipse page under the section "Importing a Zipped Project into Eclipse" to get the entire project into your Eclipse workspace.

You will see a project calledÂ PolynomialÂ with the following classes in packageÂ poly:
â€¢ Node
â€¢ Term
â€¢ Polynomial
â€¢ Polytest

(Efficiency is not a requirement for any of the methods. And, you can useÂ MathÂ class methods as needed.

Observe the following rules while working onÂ Polynomial.java:
â€¢ Only fill in the code in the methodsÂ add,Â multiply, andÂ evaluateÂ where indicated.
â€¢ In methods that return aÂ PolynomialÂ (addÂ andÂ multiply), the polynomial that is returned must be represented as described in the "Notes about representation" part of theÂ BackgroundÂ section above.Â â€¨Your method will not get creditÂ if the returned polynomial does not adhere to this representation, even it is mathematically correct.â€¨ Also see the "Notes about empty (zero) polynomials" at the end of theÂ Running the programÂ section below.
â€¢ DO NOTÂ remove the import statements at the top of any of the given classes.
â€¢ DO NOTÂ add any import statements to the original list of imports inÂ Polynomial.java
â€¢ DO NOTÂ change the headers of ANY of the given methods
â€¢ DO NOTÂ change/remove any of the given class fields
â€¢ DO NOTÂ add any new class fields.
â€¢ YOU MAYÂ add new helper methods, but you must declare themÂ private.
â€¢ Do not changeÂ NodeÂ andÂ TermÂ in any way. You will not be submitting them, and we will be using the original versions to test yourÂ PolynomialÂ implementation.
â€¢ If you wish to changeÂ Polytest, feel free. You will not be submitting it, and we will not be using it to grade yourÂ PolynomialÂ submission.

Running the program
There are three sample input files for you to test (they should be under the project folder in Eclipse):Â
â€¢ A fileÂ ptest1.txtÂ that contains the polynomial4x^5 - 2x^3 + 2x + 3â€¨
â€¢ A fileÂ ptest2.txtÂ that contains the polynomial8x^4 + 4x^3 - 3x + 9â€¨
â€¢ A fileÂ ptest1opp.txtÂ that contains the polynomial-4x^5 + 2x^3 - 2x - 3â€¨(the negation of the polynomial inÂ ptest1)

In each of these files, each line is a term, with the first value being the coefficient, and the second value being the degree. The terms are listed inÂ descendingÂ order of degrees and the respective non-zero coefficients. Remember that when you store a polynomial in a linked list, you will store it inÂ ascendingÂ order of degrees. (This is actually already implemented by the Polynomial constructor when it reads a polynomial from an input file. All you have to do is make sure you stick with this rule when you add and multiply.)

You may assume that we will NOT test with an invalid polynomial file, i.e. every test input file will either have at least one term in the correct format or will be empty (seeÂ Notes about empty (zero) polynomialsÂ below). So you don't need to check for the validity of the input.

Download the attachedÂ polynomial_project.zipÂ file to your compute...