Algebra

Algebra is the branch of mathematics that studies variables and constants. Algebra also refers to generalisation of arithmetic. It uses algebraic structures and algebraic operations.
The word algebra derived from the Arabic book of Abu Abdullah Mohammad Ibn Musa al-Khwarizmi, a persian scientist amd mathematician where he described a method of solving equations in his book al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabalah.

Algebra topics list

1. Algebraic expressions
2. Polynomials
3. Equations

1. Algebraic expressions

Algebraic expressions are a mix of variables and constants concatenated with arithmetic operations. Whole algebra is based on algebraic expressions. A complete detail of algebraic expressions and how the four fundamental operations of addition, subtraction, multiplication and division are performed on them can be studied in Algebraic Expression and its Operations with Examples

2. Polynomials

Polynomials in algebra are the algebraic expressions in which all variables involved in it have powers with whole numbers only. Definition of polynomial and types of polynomial can be found in Polynomial, its Terms, Degree and Types.

These polynomials in algebra are represented by curves, when drawn graphically. These curves when cut x-axis, the value of x of such points on x-axis are called zeros of the polynomial.

Further, the sum and product of all zeros of a polynomial always give constant values which has a relationship to the coefficients of variables of the polynomial. Learn here to find out how coefficients of polynomial are related to sum and product of its zeros.

3. Equations

Equations in algebra is a condition when two algebraic expressions are equated with sign of equality (=). They are solved to find the value of their variable (e.g. x or y). Linear equations which have the highest power of x can be solved with three methods:

1. Trail and error method
2. Systematic method
3. Transposition method

The chapter Linear Equation with Examples and Methods to Solve explains what is linear equations and the three methods to solve them.

The other type of equations are the quadratic equations which have the highest power of 2 of their variables. Again, there are three methods to solve the quadratic equations:

1. Factorization method
2. Completing the square method
3. Quadratic formula method

The basics of quadratic equations with details of the methods to solve and how to find the roots of the quadratic equations are worth to read in the chapter Quadratic Equation. Find Roots and Methods to Solve.