Today is our topic of discussion Algebraic Expression .
Algebraic Expression
We are familiar with various types of algebraic expressions. When one or more numbers and symbols representing numbers are combined meaningfully by one or more than one of +, -, x,, power or rational sign, a new symbol representing numbers is created. It is called an algebraic expression or in brief expression. For example, each of 2x, 2x + 3ay, 6x+4y²+a+ √z etc, is an algebraic expression. At the end of this chapter, students will be able to –
- explain the concept of a polynomial;
- explain with example the concept of a polynomial with one variable;
- explain multiplication and division of polynomials;
- explain the remainder theorem and the factor theorem and apply to factorize a polynomial;
- explain homogeneous expressions, symmetric expressions and cyclic
Variable, Constant and Polynomial
In any discussion, a literal symbol representing a number may be a variable or a constant. If such a symbol denotes any unscheduled element of the number set consisting of more than one elements we call the symbol a variable and the set is called the domains. If the symbol denotes a definite number, it is called a constant. In any discussion a variable can take any value from its domain, but the value of a constant remains fixed all through.
A polynomial is a special type of algebraic expression. In a polynomial there are one or more terms and each term is a product of a constant and a non-negative integral power of one or more variables.
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