The study of polynomials is an important part of the mathematics curriculum in CBSE class 10th curriculum. The algebraic expressions are included in the study to provide an understanding of the properties of polynomials.
In the ncert solutions for class 10th maths chapter 2, you get introduced to the concepts related to the types of polynomials. One of the important concepts is the categorization of the polynomials according to the degree it has.
Before we start understanding the types of polynomials, it becomes important to understand the degree of a polynomial.
What is the degree of a polynomial?
In a polynomial, the exponent of the highest power of the variable becomes the degree of that polynomial. This degree helps in understanding the types of polynomials.
What are the types of polynomials?
- Zero polynomial
A zero polynomial has all the coefficients as zeros. This means that every term in a zero polynomial becomes zero.
- Constant polynomial
When a polynomial has only one term, which is a real number, then, it is called a constant polynomial. The unavailability of the variables makes it constant. Hence, a constant polynomial is basically a real number.
- Linear polynomial
A linear or a first-degree polynomial has a degree of one. This means that the linear polynomial has two terms where one term has a variable of exponent 1 and the other term is any real number including 0. An important fact to know here is that the coefficient of the variable can’t be 0.
- Quadratic polynomial
A polynomial with a degree of two is what you call a quadratic polynomial. This means that the polynomial has to have a variable with exponent power 2 with a non-zero coefficient. In the general form, these polynomials have at least one term of degree 2.
- Cubic polynomial
When a polynomial has a degree of 3, it is called cubic polynomial. A cubic polynomial has one term where the variable has the maximum exponent power of 3. This term has to have a non-zero coefficient in order to keep the third-degree form. Other terms can have any real number coefficients.
- Bi-quadratic polynomial
Bi-quadratic is a polynomial with the degree of four. Hence, the maximum power of the polynomial variable is 4, along with a non-zero coefficient. All the other terms can have any real number coefficients.
Other valuable terms related to the polynomials
- Value of a polynomial
The value of a polynomial is achievable by inserting a real number in the place of the variable. The insertion of the real number allows you to solve the polynomial and attain a solution. That solution is called the value of that polynomial for that real number value of the variable.
- Zero of a polynomial
Any real number that can make the value of the polynomial zero is called the zero of the polynomial. The real number is placed where the variables are in order to get the 0 value.
For in-depth study, you need to attain valuable study materials of the cbse class 10 maths polynomials.