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Polynomial for Class 10

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All Types of Polynomials

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Polynomials are algebraic expressions that may consist of exponents, variables, and constants that are added, subtracted, or multiplied. These elements of the polynomial are combined using mathematical operations such as addition, subtraction, multiplication, and division (No division by a variable). Polynomials are of different types which are namely Monomial, the Binomial, and the Trinomial. A monomial is a polynomial consisting of only one term. A binomial is a polynomial with two dissimilar terms. A trinomial is an algebraic expression consisting of three dissimilar terms.


Polynomial Equation

An algebraic expression of one or more mathematical terms each of which comprises of a constant multiplied by one or more variables raised to the power of a nonnegative integral (such as m + nx + ox2).


What is Unique About Polynomials?

Because of the rigid description, polynomials are quite easy to work with.

For example, we are aware of:

If you add polynomials you obtain a polynomial.

If you multiply polynomials you obtain a polynomial.

So you can do ample operations of additions and multiplications, and still have a polynomial as an outcome.

More so, polynomials of one variable are easy to plot on the graph, as they have even and steady lines.


Types of Polynomials

Let us get to know the different kinds of polynomials as getting familiar with these will help form the base for further learning.

  • Binomials – Binomials is what we call algebraic expression that consists of two dissimilar terms, thus the name “Bi” nomial. For instance, 2x + 5x2 is binomial given that it contains two dissimilar terms, that is, 2x and 5x2. In the similar manner, 8pq + 19p2q is a binomial.

  • Monomials – Monomials are said to be algebraic expressions that consist of one term, thus the name “Mono” mial. That is to say, it is an algebraic expression that has any count of like terms. For example, 4x + 7x + 12x is a monomial since when we add the like terms it will result in 23x. Moreover, 4t, 21a2yb, 9ab, etc are monomials since each of these expressions has only one term.

  • Trinomials – Trinomials are algebraic expressions with three unlike terms, hence the name “Tri” nomial. For example- 3x + 5x2 – 6x3 is a trinomial. It is simply because of the existence of three dissimilar terms, namely, 3x, 5x2, and 6x3. In the same way, 12pq + 4x2 – 10 is a trinomial.

There is another type of polynomial known as the zero polynomial. In this form of a polynomial, the value of every coefficient is zero (0). For example: 0x2 + 0x – 0.


Degree of a Polynomial Definition

In order to define the degree of a polynomial, it is simply the greatest of the exponents or powers over different terms that exist in the algebraic expression.

Example: Evaluate the degree of the expression 7x – 5.

In the example provided above, the 1st term we have is 7x, while the 2nd term is -5. Now, let us describe the exponent for each term of the expression. The exponent for the 1st term 7x is 1 and for the 2nd term -5 is zero (0). Now that the highest exponent is 1, the degree of equation 7x – 5 is also 1.


Solved Examples For You

Question 1: Which of the following is a binomial?

a. 8*p + p          b. 7p2 + 8q + 9r

c. 3p*4q* 2r    d. 11p2 + 11q2

Answer : d. 11p2 + 11q2

a) 8p + p will provide 9a which is a monomial.

b) 7p2 + 8q + 9r is a trinomial.

c) 3p*4q* 2r will give 24pqr, which is also a monomial.

d) 11p2 +11q2 is a binomial.

FAQ (Frequently Asked Questions)

Q1. What is Meant by a Polynomial?

Answer: In simple terms, polynomials are algebraic expressions having a sum of terms, where each term bearing a variable or variables is raised to the power and moreover multiplied by a coefficient. Interestingly, the simplest polynomial carries one variable.

Q2. Who First Discovered Polynomials?

Answer: Polynomials was introduced by Rene Descartes in 1637. The French-born mathematician and scientist is responsible for inventing the concept of the graph of polynomial equations in La geometric. In addition, prior to this, there was the multiplication of polynomials taking place in the 15th century where they quoted equations in words.

Q3. What is Meant by a Zero Polynomial?

Answer: A zero polynomial is basically a constant polynomial all of whose coefficients are equivalent to 0 (zero). That said, an equal polynomial function is a constant function which consists of value 0, which we also refer to as the zero maps. Hence, the zero polynomial is said to be the additive identity of the additive category of polynomials.

Q4. Which is a Polynomial with 5 Terms?

Answer: Expressions consisting of more than three terms are labelled solely by its number of terms. For example, a five-term polynomial is a polynomial which consists of five terms. On the other hand, a quadrinomial that merely consists of 4 terms is said to be a Quadri polynomial.