Explain how linked lists can be used to represent polynomials. Provide an example and describe the addition of two polynomials. give the answer for 5 marks

Linked lists can be used to represent polynomials in a very efficient way. Each node of the linked list can represent a term of the polynomial. The node can contain two fields: one for the coefficient of the term and the other for the power of the term. The linked list can be sorted in decreasing order of powers so that the first node contains the highest power of the variable.

For example, consider the polynomial 3x^3 + 2x^2 + 5x + 10. This can be represented as a linked list where the first node contains the coefficient 3 and power 3, the second node contains the coefficient 2 and power 2, the third node contains the coefficient 5 and power 1, and the fourth node contains the coefficient 10 and power 0.

Adding two polynomials using linked lists involves creating a new linked list that contains the sum of the coefficients of the terms with the same power from the two polynomials. You start from the beginning of both lists and compare the powers of the terms. If the powers are the same, you add the coefficients and insert a new node in the result list with the sum of the coefficients and the common power. If the powers are different, you insert a new node in the result list with the coefficient and power from the list that contains the higher power, and move to the next node in that list. You continue this process until you have processed all the terms in both polynomials.

For example, consider adding the polynomials 3x^3 + 2x^2 + 5x + 10 and 4x^3 + 3x^2 + 2x + 1. The result is a new polynomial 7x^3 + 5x^2 + 7x + 11, represented as a linked list with nodes (7,3), (5,2), (7,1), and (11,0).