Polynomial

• A polynomial is an algebraic expression where the exponents of its variables are whole numbers.
• What Expressions Are NOT Polynomials?

  • Expressions with fractional or decimal exponents in the variable are not polynomials
  • Expressions with negative exponents in the variable are not polynomials
  • Expressions with variables in the denominator are not polynomials
  • Expressions with variables under the radical sign are not polynomials
• Terms of a Polynomial

  A term in a polynomial consists of a number multiplied by a variable with a whole number exponent.

  
• The name polynomial comes from “poly” (Greek) which means many, and “nomen” (Latin) which means name (in this case, “term”). This means that a polynomial consists of different terms.
• 5y2 and 3y2 are like terms because these terms have the same variable (y), and their exponents are the same (which is 2).

  On the other hand, 7x2 and 5a2 are not like terms because these terms have different variables.
• The degree of a polynomial is the highest exponent of the variable of a polynomial.
• Types of Polynomials According to the Number of Terms

  A) Monomial

  B) Binomial

  C) Trinomial

  D) multinomial

  
• Types of Polynomials According to Degree

  A) Constant

  B) Linear

  C) Quadratic

  D) Cubic

  E) Quartic

  F) Quintic

  
• A polynomial is written in its standard form if the terms of the polynomial are arranged in a manner where the exponents of the variable are in decreasing order.
• If we express a polynomial in its standard form, the first term of that polynomial is called the leading term