Polynomials are an essential part of math studies to get a basic understanding of various math topics. It is the basic building block of almost every type of mathematical expression, such as rational expressions. The concept of polynomials is applied in several things in our daily life. Many routine calculations can be interpreted as polynomials. We use polynomials without realizing it in supermarkets, banking, driving, etc. The concept of polynomials is also useful in construction work, business, implementation of traffic lights, etc. Some mathematical applications of polynomials include representation of the perimeter, area, and volume of geometric figures.
Polynomials are even studied in other subjects like economics, chemistry, and physics. In physics, polynomials are used to measure acceleration and represent units of energy, electricity, etc. In chemistry, these polynomials are used in writing and balancing chemical equations. In economics, polynomials are used in modeling stock markets, expense budgeting, etc. Normally people think that polynomials are only applicable to the higher-level mathematics courses but actually, it is not so because these are also very much applicable in the day to day life of the people. There are different kinds of fields of industries that utilise polynomials in the whole process to ensure that they will be settling the most accurate calculations.
The chemists also use polynomials in terms of determining the combination of different kinds of compounds as well as molecules so that overall purposes are easily achieved. The statistical formulas also use the polynomials into different kinds of ascertaining future values so that accurate results are always found. The astrophysicists also utilise polynomials in terms of regulating the velocity of the star as well as the distance of one object from the other in space. Computer scientists also utilise this particular concept to ensure that scientific calculations are perfectly undertaken and the best of the decisions are always made.
What are polynomials?
A polynomial is an algebraic expression that comprises variables and exponents involving operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The degree of a polynomial is the highest power of an algebraic expression. To find the degree of a polynomial, you have to find the largest exponent in the polynomial to write it in a standard form. Finding the degree of a polynomial requires adding the variables’ powers in each term; it is not required that they are the same variables.
Classification of Polynomials:
Polynomials are primarily a sequence of mathematical terms added together. Each term usually contains one or more variables raised to some exponential powers with a coefficient associated with it. Polynomials can be both simple and complex expressions with higher degrees. They are often written in a standard form with terms in higher degrees, followed by the term with the smaller exponent. The coefficient associated with the term with the highest power is called the leading coefficient. A polynomial that doesn’t contain any variable is called a constant. Classifying the polynomials requires determining their degrees and number of terms. Polynomials can be classified into different types depending upon their degree and the number of terms involved.
Types of polynomials based on the degree:
The highest value of the exponent in an expression is known as the degree of Polynomial or order of the polynomial. While finding the degree of the polynomial, the terms should be arranged in either ascending or descending order. Based on the degree of the polynomial, polynomials can be classified into four major types:
- Zero or Constant Polynomial: A constant polynomial is a polynomial without a variable which means it has only a constant part. For example, 2, -5, etc. Since there is no variable in such polynomials, we can say it is a polynomial with zero degree.
- Linear Polynomial: The polynomial expression whose degree is one is called a linear polynomial—for Example, 2x+7 or 6y+3.
- Quadratic Polynomial: The polynomial expression with the highest degree as two is called a quadratic polynomial. For example, 2x² + 5 or 16y² + 7.
- Cubic Polynomial: The polynomial expression whose degree is three is called a cubic polynomial. For example, 7x²y + 5x+2,
Types of polynomials based on the number of terms
Polynomials are classified and named based on the number of terms it has. Some types of polynomials have specific names indicated by their prefix.
- Monomials: Mono means one, and a monomial is a polynomial with exactly one term. For example, 4, 3x, 4x²y, etc.
- Binomials: Bi means two, and binomial is a polynomial with exactly two terms. For Example, 4x+5.
- Trinomials: Tri means three, and trinomial is a polynomial with exactly three terms. For Example, 2x²y+4x+9. The prefix of the word “polynomial” is poly which means many. However, the word polynomial can be used for all numbers of terms, including monomials.