Algebra

Polynomials

Methods of factorization of a polynomial: factoring out a common factor, abbreviated multiplication formulas, grouping

            Abbreviated multiplication formulas

Dividing a polynomial by a polynomial

            Dividing a polynomial by a polynomial by a column (angle)

            Method of undetermined coefficient

            Division of a polynomial by a binomial according to the Horner scheme

            Using the Horner's scheme to decompose a polynomial by powers of a binomial

            Calculating the value of a polynomial at a given point using Horner's scheme. Bezout's theorem

Factorization of polynomials

Factorization of a third degree polynomial

Equations with one variable

Equations with one variable, equivalent equations

General methods for solving equations

Algebraic equations

Linear equations

Quadratic equations, biquadratic equations

            Solving incomplete quadratic equations

            Solving complete quadratic equations

            Vieta's theorem for solving quadratic equations

            Solving of biquadratic equations

Cubic equations

            Solving cubic equations by factorization

            Solving symmetric cubic equations

            Cardano's formula for solving cubic equations

Quartic equations

            Solving equations of the fourth degree by factorization

            Solving of symmetric equations of the fourth degree

            The Ferrari's method for solving equations of the fourth degree

Equations of higher degrees

Fractional-rational equations

Equations with modulus

Irrational equations

Transcendental equations and inequalities

Trigonometric equations

Exponential equations

Logarithmic equations

Solving combined equations and inequalities

Systems of equations

Systems of two linear equations with two unknowns

Systems of three linear equations with three unknowns

Cramer's formulas for solving systems of linear equations

Solution of systems of linear equations by Gauss method

Functions

Linear

Quadratic

Cubic

Power

Hyperbolic

y = √x

Trigonometric

Exponential

Logarithmic