# Learning Basic Algebra Free

## Algebra is one of the main branches of mathematics, and concerns the study of structure, relation and quantity. It studies the property of adding and multiplying numbers, variables, and polynomials, along with their factorization and determining their roots. In addition to working directly with numbers, algebra also covers symbols, variables, and set elements. Addition and multiplication are common operations, but their precise definitions lead to structures such as groups, rings, and fields.

Basics of Algebra

Arithmetic

Addition is the basic operation of arithmetic. In its simplest form, addition combines two numbers, the addends or terms, into a single number, the sum of the numbers.

For example, the opposite of 7 is -7, so 7 + (-7) = 0.

Subtraction (−)

Subtraction is the opposite of addition. Subtraction searches the difference between two numbers, the minuend minus the subtrahend. If the minuend is larger than the subtrahend, the difference will be positive; if the minuend is smaller than the subtrahend, the difference will be negative; and if they are equal, the difference will be zero.

For example, the opposite of 7 is -7, so 7 + (-7) = 0.

Multiplication (×, •, or *)

Multiplication is the second basic operation of arithmetic. Multiplications also combine two numbers into a single number, the product. The two numbers are called the multiplier and the multiplicand, sometimes equally simply called factors.

Equations

An Equation is a math statement that asserts the equality of two expressions. Equations consist of the expressions that are to be equal on opposite sides of an equal sign, as in

For Example: x+3 =5

9-y=7

One use of equations is in math identities, assertions that are true independent of the values of any variables contained within them. For example, for any given value of x it is true that

Polynomials

A polynomial function is a function that can be defined by evaluating a polynomial. A function ƒ of one argument is called a polynomial function if it satisfies

f(x) = anxn+an-1xn-1+…+a2×2+a1x+a0For all arguments x, where n is a non-negative integer and a0, a1,a2, …, an are constant coefficients. Polynomial equations A polynomial equation is an equation in which a polynomial is set equal to another polynomial.3×2+4x-5=0 is a polynomial equation. For example, the function ƒ, taking real numbers to real numbers, defined by f(x) =x3-xis a polynomial function of one argument.

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