Ⅰ Operation of polynomials

01 Polynomial Operations
- Addition and subtraction of polynomials
- Multiplication of polynomials
- Multiplication formula (1), (2)
- Variation of the multiplication formula
- Division of polynomials
- Assembly method
02 Remainder Theorem
- Identity
- Remainder theorem
- Takeover theorem
03 Factorization
- Factoring formula (1), (2)
- Factorization using substitution
- Factorization of expressions with multiple characters
- Factoring of higher-order equations
- Application of factorization

Ⅱ Equations and Inequalities

01 Complex Numbers and Quadratic Equations
- Complex number
- Complex number calculation
- power of i
- Square root of a negative number
02 Quadratic equations and quadratic functions
- Solving linear equations
- Solving quadratic equations
- Discriminant of quadratic equation
- Relationship between roots and coefficients of quadratic equations
- Properties of conjugate roots of quadratic equations
03 Various equations
- Graph of quadratic function
- Relationship between quadratic functions and quadratic equations
- Positional relationship between the graph of a quadratic function and a straight line
- Maximum of a quadratic function.
Minimum
- Maximum and minimum of quadratic function in limited range
04 Various inequalities
- Cubic and quartic equations (1), (2)
- Relationship between roots and coefficients of cubic equations
- Imaginary roots of the equation x³=1
- Simultaneous linear equations
- Simultaneous quadratic equations
- Symmetry and indefinite equations
- Basic sincerity of inequality
- Solution to first-order inequality
- Relationship between quadratic functions and quadratic equations
- Solution to quadratic inequality
- Application of quadratic inequalities
- Simultaneous quadratic inequalities

Ⅲ Number of cases

01 Number of cases
- Cases (1), (2)
02 Permutations and Combinations
- Permutation
- Combination
- Division and distribution

Ⅳ matrix

01 matrix
- Meaning of matrix
- Same matrix
- Addition and subtraction of matrices
- Real multiple of the matrix
- Matrix multiplication
- Properties of matrix multiplication
- Cayley-Hamilton theorem