The expression ‘ ’ is a polynomial of degree 3. For example, the expression ‘2x+1’ is a polynomial of degree 1. The highest power to which a variable is raised in a polynomial is called the degree of the polynomial. It is known as a constant polynomial.įrom now on, in this article, by ‘polynomial’ we would mean ‘a polynomial of single variable’. Interesting fact: A constant e.g., 3 can also be referred as a polynomial. Mark and classify the variables, coefficients and constants in the polynomials. For example, is a polynomial of three variables.Įxercise: Identify which among the following expressions are polynomials. Three, that there can be more than one variable in the expression of the polynomial.

Note that constants as well as coefficients are not mandated to be whole numbers. Therefore, is not a polynomial since one of the exponents i.e., is not a whole number. Two, that the exponents must be whole number. Therefore, is not a polynomial since it contains negative exponent of the variable x. One, that the variables are raised to only positive exponents.

There are certain aspects that characterize the polynomials. In the polynomial, only the number 8 is a constant. In the polynomial, 3 and 2 are the coefficients.Ĭonstants: The real numbers that appear standalone (without the variable) are called constants. They are also called Indeterminates since they do not have a specific value.Ĭoefficients: In simple words, the real numbers that appear with the variables are called coefficients. The letters x, y and z are generally used to represent the variables. They act as placeholder in mathematical equations. Variables (or Indeterminates): The entities that can take on value of any real number are known as variables. The variables are raised to whole number exponents/powers.įor example, the given expression is a polynomial of one variable (x) only. DefinitionĪ polynomial is a mathematical statement that consists of variables and real numbers (constant and coefficients). A number of advancements were carried out by several mathematicians and physicists after then. World renowned mathematician Newton (1643-1727) also contributed a lot in this field. In 16th century A.D., the solution to the polynomial equations with degree higher than two was accomplished by European mathematicians including Cardano (1501-1576) and Ferrari (1522-1565). Later, during the “Dark Age” of the Europe, eminent Muslim scientists such as Al-Khowarizmi (800-847 AD), Al-Karaji (953-1029) and Al-Samawal (1130-1180) invented and applied the concept of notations to perform different calculations. The problems that we now represent as polynomial equations were known and even solved in the ancient era as early as 250 AD. The roots of the word “polynomial” date back to 17th century when it was first used. As you can see that it is hard to make anything out of the literal meaning of the word. Thus, the word “polynomial” means “ many names”. The word polynomial is an amalgamation of a Greek word, “poly” (meaning many) and Latin “nomen” (meaning name). Without understanding the concept of polynomials, it is hard to move ahead in complete understanding and application of mathematics. In fact, polynomials form an essential part of algebra. You will find them frequently in your maths textbooks. They help to reduce complex problems into the form of letters and numbers, that are easy to manipulate and work with. 7 More on the graphs of Quadratic polynomial