FAQs of Polynomial
What is a Polynomial?
A polynomial is an expression that involves variables (usually represented by letters) raised to powers and combined using addition, subtraction, and multiplication. The variables can have coefficients (numbers multiplying the variables) attached to them.
What are Examples of Polynomial?
Some examples of polynomials are:
- 3x2 + 2x – 1,
- 4y3 – 5y + 2,
- 7a4 – 2b2, etc.
What is Zero of Polynomial?
Zeros of a polynomial is a the value of the polynomial substituting it in the polynomial results in Zero. Suppose we have a polynomial P(x) then zero of the polynomial is ‘a’ if P(a) is zero.
What is Coefficient of a Polynomial?
In a variable there are various terms and the coefficient of each term is called the coefficient of a polynomial. For example, in a polynomial x2 + 2x + 3
- Coefficient of x2 is 1
- Coefficient of 2x is 2
What is Leading Coefficient of a Polynomial?
The coefficient of the highest degree term in the polynomial is called the leading coefficient of a polynomial.
What are Monomials, Binomials and Trinomials?
- Monomials are the polynomial with only one term. Example: 3x2
- Binomials are the polynomial with two terms. Example: 3x2 + 2x
- Trinomials are the polynomial with three terms. Example: 3x2 + 2x + 1
What is Constant in a Polynomial?
The constant term in the polynomial is the term with no variables. Suppose in the example, 3x2 + 2x + 1. The constant term is 1.
What are Polynomial Equations?
Equations which contains plynomials are called the polynomial equations various examples of the polynomial equations are,
- 3x3 + 8x – 5 = 0
- x + y + z = 0
- 3x + y – 5 = 0, etc.
The number of polynomials with zeros as ‒2 and 5 is?
There is 1 polynomial with zeros as -2 and 5, which is x2−3x−10.
Polynomials – Definition, Standard Form, Types, Identities, Zeroes
Polynomials: In mathematics, polynomials are mathematical expressions consisting of indeterminates (also called variables) and coefficients, that involve only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. They are used in various fields of mathematics, astronomy, economics, etc. There are various examples of the polynomials such as 2x + 3, x2 + 4x + 5, etc.
In this article, we will learn about, Polynomials, Degrees of Polynomials, Examples of Polynomials, Zeros of Polynomials, Polynomial Equations, and others in detail.
Table of Content
- What are Polynomials?
- Polynomials Definition
- Polynomials Examples
- Characteristics of Polynomials
- Standard Form of a Polynomial
- Degree of a Polynomial
- Degree of Single Variable Polynomial
- Degree of a Multivariable Polynomial
- Terms in a Polynomial
- Types of Polynomials
- Properties of Polynomials (Theorems of Polynomials)
- Operations on Polynomials
- Addition of Polynomials
- Subtraction of Polynomials
- Multiplication of Polynomials
- Division of Polynomials
- Factorization of Polynomials
- Methods of Factorization of Polynomial
- Greatest Common Factor (GCF)
- Substitution Method
- Grouping Method
- Difference of Two Squares Identity
- Zeros of Polynomial
- How to Find Zeros of Polynomials?
- Linear Polynomial
- Quadratic Polynomial
- Cubic Polynomial
- Higher Degree Polynomial
- Polynomial Identities
- Polynomial Equations
- Solving Polynomials
- Polynomial Functions
- Polynomials Class 9 Extra Questions
- Polynomials Class 10 Extra Questions
- Practice Problems on Polynomial
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