Polynomials in Algebra

What are Polynomials in Mathematics?

In mathematics, we have different types of terms. We have variables, constants, expressions, equations, coefficients, and many more.

We perform various types of operations, arithmetic calculations on these objects.

Before we come to polynomials, we must understand some of these terms.

  • Constant is a term given to an entity whose value does not change and remains the same all the time.
    • Examples: 5, -9, 0.5, 1/3 etc.
  • Variable is a term given to an entity whose value changes with time and conditions.
    • Examples: x, y, p, a, b, etc.
  • A coefficient is a number that is multiplied with variables to increase or decrease their values.
    • Example: 2 is a coefficient of x in (2x)
  • An expression is any combination of constants, variables along with the coefficients by addition or subtraction.
    • Examples: (2x+7y-8), (a+b+c), (2p-1) etc.
  • When an expression is assigned to a value or equalized with another expression, it is called an equation.
    • Examples: (2x+7y-8 = 5), (a+b+c= 2p-1) etc.

What is Polynomial?

Polynomial is a general term given to expressions where constants and variables are combined by multiplication, addition, and/or subtraction.
Poly means more than one.
Nomial is used for a term or name

When we have one or more terms in an expression then it is called a polynomial.
  • When there is only one term in an expression, it is called a monomial.
    • Example: (2x; 4p; 7; a) etc. are monomials.
  • When there are two terms in an expression, it is called binomial.
    • Examples: (2x+y; 4p-9; a+5) etc. are binomials.
  • When there are three terms in an expression, it is called trinomial. and so on.
In general, we call such expressions with one or more terms polynomials.
Algebra is a branch of mathematics where we deal with the variables. And polynomials are part of algebra.