Equivalent expressions of polynomials

Along with the development of Algebra, which was a word taken from a medieval book written in 820 AD by a Persian mathematicians, Polynomials were also created. Polynomial comes from two Greek words: Poly and Nomos which means many and parts respectively. Polynomials are expression that is comprised of a coefficient, a constant, variables and exponents. These terms can be combined through the four different operations namely addition, subtraction, multiplication and division with the exemption of division wherein the denominator is a variable.

A polynomial can be classified according to the number of terms is has: a monomial where there’s only one term like 1, 2x, and 5x25x^{2}, a binomial which is the sum of two monomial like 5x + 1, and trinomial which is the sum of three monomials like 5x + 3y + 1.

Given that a polynomial is comprised of several terms, it’s also very useful to familiarize yourself with the degree of a term and the degree of a polynomial. A degree of a term is simply the exponent that the term has like in 5x, the degree is 1. Degree of a polynomial on the other hand is the highest degree of a term, say if you have 5x4+8x33x+15x^{4}+8x^{3}3x+1, the degree of the polynomial is 4.

This chapter is consisted of three parts, in the first part we will be able to see more example of polynomials and will be able to identify whether or not it is a polynomial. We are also going to look for the degree of the term and the degree of the polynomial. In the second part we would, be looking for the coefficient of the term and also to identify like terms so we could combine them and simplify these terms. In the last part of the lesson, we would be learning on how to add and subtract polynomials which is in preparation for a more in depth discussion in the next chapters.

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Equivalent expressions of polynomials

A polynomial may contain multiple terms. The variable terms have a coefficient and a variable. Terms with the same variables are called like terms, and they can be combined together. It allows us to write equivalent expressions of polynomials with more or less terms.


  • 1.
    Identify the coefficient and the number of variables for each expression.
  • 2.
    Find the like terms.
  • 3.
    Combine like terms.
  • 4.
    4. Write an equivalent expression with seven terms for each polynomial.
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Equivalent expressions of polynomials

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