Table of Contents
What is a Polynomial?
Polynomial Definition: Polynomial is an important chapter of Mathematics that contains variables that are also known as indeterminates and coefficients that mainly consist of the operations of addition, multiplication, etc.
In order to elaborate on this topic of Polynomial definition, it can be said that it is a numeric expression consisting of one or more terms with a non-zero coefficient. An instance of Polynomial of a single indeterminate x is x2 – 4x + 7. You can also consider the real numbers as polynomial; however, it has to be a whole number when it comes to an exponent of the Polynomial.
This particular part can be defined as the highest degree of a monomial along with a Polynomial. It is the reason why a polynomial equation possesses the largest exponent is defined as a degree of polynomial.
Here is a table students can also refer to under the basic concept of the degree of a Polynomial definition.
Degree of Polynomial
| Polynomial | Degree | Example |
| Constant or Zero Polynomial | 0 | 6 |
| Linear Polynomial | 1 | 3x + 1 |
| Quadratic Polynomial | 2 | 4×2 + 1x + 1 |
| Cubic Polynomial | 3 | 6×3 + 4×3+ 3x + 1 |
| Quartic Polynomial | 4 | 6×4 + 3×3 + 3×2 + 2x + 1 |
Types of Polynomial
This particular chapter has three different types, which includes:
- Monomial implies an expression with a single term. The key aspect for this one is that the single term should be a non-zero term here. Example: 5x, -3xy, etc.
- binomial is an expression with two terms. This is mainly a difference or a sum of two or more polynomials. Example: x2 + x, y + 2, etc.
- Trinomial that means expression with three terms. Example: xy2 + xy.
One of the essential factors to keep in mind is that different subtypes of polynomials can be combined using subtraction, addition, division; however, it should never be divided by a variable.
Polynomial Equations
When it comes to Polynomial Definition in math, the equations play a significant role. These equations contain multiple variables and constants and should be practised properly to attain a decent score. The standard form of stating a polynomial that students can refer to is putting the highest degree first, and the constant term in the end. An example of that will be, b = a4 +3a3 – 2a2 + a + 1.
Polynomial Functions
‘Poly’ signifies many, and ‘nominal’ means terms, therefore, it is quite self-explanatory that gives away the fact that it is constructed with one or more terms.
Here is an idea of how the function with one variable and degree will look like:
f(x) = a0xn + a1xn-1 + a2xn-2 + ….. + an-2x2 + an-1x + an.
Polynomial Operations
Students can find mainly four sub-types of Polynomial operations, such as Addition of Polynomials, Subtraction of Polynomials, Division of Polynomials, and Multiplication of Polynomials.
The first one mainly results in a polynomial of the same degree and consists of terms like variable and power. The second one is almost similar to the first one; however, the difference is in the type of operation. Even though the result can be or not be a polynomial in case of the third one, when it comes to the multiplication of Polynomials, the result always turns out to be a polynomial of higher degree.
The basic meaning of Polynomial in Math should be explained by an algebraic expression that has variables and coefficients. Students usually find the core areas of Polynomials Definition fascinating, especially those inclined to pursue the subject in their higher education.
