Polynomials are widely used in mathematics and physics. Mathematically, a polynomial is a function of an integer, its domain is an integer, and its range is a real number. Each term of a polynomial can be expressed as the product of the power of a variable and the coefficient. For a given polynomial, we can perform various operations, such as addition, subtraction, multiplication and division.
Polynomial is a very basic concept in algebra. For example, we can solve a linear equation with one variable, which involves the root of a linear polynomial. In addition, when calculating probability, polynomials are often used to express the possibility of events.
In physics, polynomials can be used to describe many phenomena, such as elastic modulus in elasticity, resistance in electromagnetism, sound speed in acoustics and so on. In addition, in computer science, polynomials are often used for data fitting, encryption and decryption.
Properties of polynomials:
1, linear property: every term of a polynomial is linear, that is, every term can be expressed as the product of a variable (or a set of variables) and a coefficient. This property makes polynomials widely used in various mathematical and scientific calculations.
2. Additivity: each term of a polynomial can be summed independently, that is, if two polynomials have the same variables, their sum is the sum of the coefficients of the corresponding terms.
3. Multiplicity: When two polynomials are multiplied, their coefficients can be multiplied accordingly, and then the results are added. For example, if two polynomials are 3x 2+2x+ 1 and 5x+4 respectively, their product is 15x 3+ 14x 2+9x+4.
4. Differentiability: If the degree of each term of a polynomial does not exceed n, then the polynomial can be regarded as a function with n differentiability ... This means that a polynomial can be derived n times at any point.
5. Integrability: If the degree of each term of a polynomial does not exceed n, then the polynomial can be regarded as an integrable function with n degrees ... This means that the polynomial can find indefinite integral at any point.
6. Symmetry: Any two polynomials can be considered equivalent if the variables are the same and the degrees are the same. This property is widely used in mathematics.