# Polynomials

Polynomials represent an unknown quantity by a variable. Usually, alphabets and some other symbols are used as variables. A variable can take any real value. For example, x, y, z are variables.

An Algebraic expression is made up of terms. A term may be a single variable or a constant or a product of a variable and a number. In general, an algebraic expression is of the form (constant) × (variable) $\frac{1}{2}$ x, x, 7x are examples of algebraic expressions. $\frac{1}{2}$ x - The variable x is multiplied by constant $\frac{1}{2}$

x - The variable x is multiplied by constant 1.

7x - the variable x is multiplied by constant 7.

If we do not know the value of the constant, then we usually use the letters a, b, c, d to represent the constant. When we say ‘ay', ‘a' represents a constant unless mentioned otherwise and ‘y' represents a variable. The value of a constant does not change but the value of a variable can change in a problem. Each term in an algebraic expression is separated by a + or - sign. A monomial is an algebraic expression with a single algebraic term. The Numerical Coefficient of a monomial is the numerical part of the monomial. For example, the velocity of an object dropped from a height of s units can be represented as v^{2} = 2gs where g is acceleration due to gravity. In this algebraic equation, v$^{2}$ and 2gs are terms. They are monomials. 2 is the Numerical Coefficient of the term 2gs. Every term in a polynomial will have a coefficient. Consider the polynomial -x + 3. This polynomial can be rewritten as -x + 3x$^{0}$ The coefficient of x is -1. The coefficient of x$^{0}$ is 3 or 3 is the coefficient of x$^{0}$