Polynomials can be used in many mathematical fields, such as algebraic operation, equation solving, interpolation and approximation. Common operations include addition, subtraction, multiplication, division and factorization. Through the operation and analysis of polynomials, we can get information about their properties, roots (zeros), images and behaviors. The concept of polynomial has played an important role in the history of mathematical development.
Around 300 BC, Euclid put forward the "square difference" in geometry, which is an algebraic expression composed of the difference between two square numbers. This can be regarded as a simple quadratic polynomial. Euclid's work laid the foundation of polynomial research and provided inspiration for later mathematicians.
/kloc-in the 6th century, the French mathematician violetta Cardin began to systematically study polynomials and their properties. He introduced the term "polynomial" for the first time in his book Algebra, and studied the concepts of roots and factorization of polynomials.
Descartes, a French mathematician in17th century, made great contributions to geometric algebra. He founded Cartesian coordinate system, transformed geometric problems into algebraic problems, and expressed curves and graphs with polynomials. /kloc-In the 8th century, mathematicians Euler, Lagrange and others further developed the polynomial theory and put forward the research methods of polynomial interpolation, root theorem and polynomial equation.
Representation of polynomials
The unary polynomial can usually be expressed as [p (x) = a _ nxn+a _ {n-1} x {n-1}+\ ldots+a _1x1+a _ 0], where
The degree of polynomial refers to the exponent of its highest power, that is, (n). If all terms of a polynomial have zero exponent, its degree is zero, which is called a constant polynomial.