Newton's Sums is a mathematical tool that relates the coefficients of a polynomial to the sums of its roots. Specifically, it provides a way to calculate the sum of the powers of the roots of a polynomial without needing to find the roots themselves. This is particularly useful in algebra for solving problems involving polynomial equations. The method is based on the idea that if you have a polynomial of degree n , you can express the sums of the roots raised to various powers in terms of the polynomial's coefficients. This connection simplifies calculations and helps in understanding the relationships between the roots and the polynomial's structure.