Syllabus covered in the MSVgo app

Download MSVgo app now!

Chapter 2 – Polynomials

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:


As we all know, the utility of algebra is increasing for students studying mathematics. This makes it important for us to understand the basics of algebra and the terms associated with it. Polynomials is one such concept we should be familiar with. You should familiarise yourself with the concepts and make yourself strong in solving questions involving polynomials. The word ‘polynomial’ has been derived from the Greek word ‘poly’ which means many and ‘nomial’ which means terms. Therefore, polynomials represent ‘many terms’. 

Polynomials is a very common term used in mathematics. In mathematics, a polynomial is an algebraic expression consisting of three types of terms: constants, exponents, and variables. A polynomial can have several variables, exponents, and constants. These terms are always combined using mathematical operations like addition, subtraction, multiplication, and division (no division operation using a variable). Understanding the concepts of polynomials is very important if a student wants to understand algebra as a whole.

For solving linear polynomials, you must be aware of the basic terms used to frame a polynomial.

Variables: a, b, c, x, y, z, etc.

Constants: 1, 2, 3, 4, 5, etc. (Constants can be the coefficients of a variable like 2x, 5a, 6c, etc.)

Exponents: x^6 is an example of an exponent.

Polynomial: x^2 – 5x + 6, 2z – 8

Let us take the example of the above polynomial.
P(x) = x^2 – 5x + 6
In the above polynomial equation, the highest exponent of a variable in a monomial is 2. Therefore, the degree of the polynomial is 2.
Thus, in a polynomial expression with one variable, the highest exponent of the monomial variable is called the degree of a polynomial.

A polynomial, as the name suggests, can have many terms. Each term in a polynomial expression is separated from the other using a mathematical operation like ‘+’ or ‘-‘.
Let us take an example.
In the polynomial expression a^3 + 6a^2 – 8a + 9, there are four different terms: a^3, 6a^2, -8a, and 9. Each of these terms is separated by a mathematical operation.

Polynomials are of three types:

  1. Monomials
  2. Binomials
  3. Trinomials

This classification is based on the number of terms in a polynomial expression. The terms in a polynomial can be combined using addition, subtraction, multiplication, and division. We cannot divide a polynomial with a variable lest it becomes a non-polynomial. 1/x, y^(-4) are examples of non-polynomials.


A monomial is a polynomial with a single non-zero term. Even a constant term is a monomial.
Example: x^2, 8c^3, 5y, 3, etc., are all monomials


A binomial is a polynomial with exactly two terms. The terms in a binomial are a sum or difference of two monomials.
Example: -8c^3 -3, 5xy^2 + 13x^3y, etc.


A trinomial is a polynomial with exactly three terms. Trinomials are a combination of monomials, separated by either addition or subtraction.
Example: x^2 – 5x + 6, -5z^4 + 2x^3 – 6, etc.

A polynomial equation is of the form an(xn). Here, ‘a’ is a coefficient, ‘x’ is a variable, and ‘n’ is the exponent.

If we expand the polynomial equation, we get:

F(x) = anxn + an-1xn-1 + an-2xn-2 + …….. + a1x +a0 = 0

Let us take an example. x^2 – 5x + 6 = 0 is a polynomial equation. Here, x^2 – 5x + 6 is the polynomial expression, which has been equated to 0.

A polynomial function is an expression created with one or more terms. It is represented as:

P(x) = an(xn)

P(x) = anxn + an-1xn-1 + an-2xn-2 + …….. + a1x + a0

Here, ‘a’ is a coefficient, ‘x’ is a variable, and ‘n’ is the exponent.

Example: P(x) = x^2

P(x) = -8c^3 -3

With the help of introductory algebra and factorization, we can solve polynomials. The first step in solving a polynomial equation is equating it with 0. We can solve two types of polynomial equation:

  1. Linear polynomial equations
  2. Quadratic polynomial equations


Solving Linear Polynomial Equations

A linear polynomial equation can be expressed in the form of ax + b = 0. Here, ‘a’ is the coefficient, ‘x’ is the variable, and ‘b’ is the constant. The degree of the equation is always 1.

To solve a linear polynomial equation, equate the polynomial to 0.

For example,

Solve for c in 2c – 4.


2c – 4 = 0 (Equation should be made equal to 0)

2c = 4

C = 4/2

C = 2

Therefore, the solution for 2c – 4 is c = 2.

Solving Quadratic Polynomials 

A quadratic polynomial equation is an equation with degree 2. It is expressed in the form ax^2 + bx + c = 0. 

To solve this equation, first arrange the terms in descending order of degree, equate it to 0, and then perform polynomial factorization to get the solution.


Solve for x in x^2 + 6 – 5x


Let us first arrange them in the decreasing order of degree

x^2 – 5x + 6

Now, we need to equate it to 0.

x^2 – 5x + 6 = 0

Now we need to perform factorization,

x^2 – 3x – 2x + 6 = 0

x(x – 3) – 2(x – 3) = 0

(x – 3)(x – 2) = 0

Therefore, x = 3 or 2.

There are four primary operations that we can perform.

  1. Addition
  2. Subtraction
  3. Multiplication
  4. Division

Let us look at an example of addition of polynomials.

To add two polynomials, we can add the coefficients of the term with the same degree of variables. The addition of two polynomials always results in a polynomial of the same degree.

Example – The sum of two polynomials 5x + 3y^2 + 7 and 2y^2 – 4 – 8x, would be given as 5y^2 + 3 – 3x.

Understanding polynomials is very important as it gives you a basic understanding of how algebra works. It also forms a major portion of mathematical analysis conducted by students regularly. Therefore, understanding the basics is the first and foremost step.

There are a lot of other concepts relating to polynomials to be explored. For more content on the subject, go to the MSVgo application, where more exciting videos with explanatory animations and texts can be found.

Download the MSVgo app and get access to a repository of learning resources. It contains multiple videos which will help in understanding and brushing up your concepts on polynomials. With the help of these videos, you will understand the core concepts required to solve questions related to polynomials. It is very important to understand these underlying concepts in mathematics if you want to efficiently and easily solve problems.

  1. What is a polynomial equation?
    A polynomial equation is of the form an(xn). Here, ‘a’ is a coefficient, ‘x’ is a variable, and ‘n’ is the exponent.
    If we expand the polynomial equation, we get;
    F(x) = anxn + an-1xn-1 + an-2xn-2 + …….. + a1x +a0 = 0
    Let us take an example. x^2 – 5x + 6 = 0 is a polynomial equation. Here, x^2 – 5x + 6 is the polynomial expression, which has been equated to 0.
  1. What are five examples of a polynomial?
    Five examples of polynomials can be:
    6x-2, x^2 – 5x + 6, x^3 – 1, X^4 + x^3 + x^2 + 1, and 2.
  1. What is not a polynomial?
    Expressions like 1/x, y^(-4) are examples of non-polynomials, which have negative exponents of variables.
  1. How do you find the degree of polynomials?
    In a polynomial expression with one variable, the highest exponent of the monomial variable is called the degree of a polynomial.
  1. How do you classify polynomials?
    Polynomials are of three types:
  1. Monomials
  2. Binomials
  3. Trinomials

This classification is based on the number of terms in a polynomial expression.

High School Physics

  • Alternating Current
  • Atoms
  • Communication Systems
  • Current Electricity
  • Dual nature of Radiation and Matter
  • Electric Charges and Fields
  • Electricity
  • Electromagnetic Induction
  • Electromagnetic Waves
  • Electron Beams and Radioactivity
  • Electrons and Photons
  • Electrostatic Potential and Capacitance
  • Fluid Pressure
  • Force and Acceleration
  • Force And Laws Of Motion
  • Gravitation
  • Internal Energy
  • Kinetic Theory
  • Law of motion
  • Light – Reflection And Refraction
  • Magnetic Effects Of Electric Current
  • Magnetism and Matter
  • Management Of Natural Resources
  • Mechanical properties of Fluids
  • Mechanical properties of Solids
  • Motion
  • Motion in a plane
  • Motion in a straight line
  • Moving Charges and Magnetism
  • Nuclear Energy
  • Nuclei
  • Oscillations
  • Our Environment
  • Paths of Heat
  • Physical world
  • Ray optics and optical instruments
  • Semiconductor Devices
  • Semiconductor Electronics: Materials, Devices and Simple Circuits
  • Simple Machines
  • Sound
  • Sources Of Energy
  • Specific and Latent Heats
  • Spherical Mirrors
  • Static Electricity
  • Systems of Particles and Rotational motion
  • Thermal properties of matter
  • Thermodynamics
  • Units and Measurement
  • Vectors, Scalar Quantities and Elementary Calculus
  • Wave Optics
  • Waves
  • Work, Power and Energy

High School Chemistry

  • Acids, Bases and Salts
  • Alcohols, Phenols and Ethers
  • Aldehydes, Ketones and Carboxylic Acids
  • Aliphatic and Aromatic Hydrocarbons
  • Alkyl and Aryl Halides
  • Amines
  • Analytical Chemistry 
  • Atomic Structure
  • Atoms And Molecules
  • Basic concepts of Chemistry
  • Biomolecules
  • Carbon And Its Compounds
  • Carboxylic acids and Acid Derivatives
  • Chemical Bonding and Molecular Structures
  • Chemical Energetics
  • Chemical Equilibria
  • Chemical Kinetics
  • Chemical Reactions And Equations
  • Chemical Reactions and Their Mechanisms
  • Chemistry in Everyday Life
  • Chemistry of p-Block elements
  • Chemistry of Transition and Inner Transition
  • Classification of Elements
  • Coordination Compounds
  • Cyanide, Isocyanide, Nitro compounds and Amines
  • Electrochemistry
  • Electrolysis
  • Elements, Compounds and Mixtures
  • Environmental Chemistry
  • Equilibrium
  • Ethers and Carbonyl compounds
  • Haloalkanes and Haloarenes
  • Hydrocarbons
  • Hydrogen
  • Ideal solutions
  • Introduction to Organic Chemistry
  • Ionic equilibria
  • Matter
  • Matter Around Us
  • Matter In Our Surroundings
  • Metallurgy
  • Metals And Non-Metals
  • Mole Concept and Stoichiometry
  • Natural Resources
  • Organic Chemistry – Basic Principles
  • Periodic Classification of Elements
  • Physical and Chemical Changes
  • Physical and Chemical Properties of Water
  • Polymers
  • Preparation, Properties and Uses of Compounds
  • Principles and Processes of Isolation of Elements
  • Redox Reactions
  • Relative Molecular Mass and Mole
  • States of Matter
  • Structure Of The Atom
  • Study of Compounds
  • Study of Gas Laws
  • Study of Representative Elements
  • Surface Chemistry
  • The d-block and f-block elements
  • The Gaseous State
  • The p-Block Elements
  • The Periodic Table
  • The s-Block Elements
  • The Solid State
  • Thermodynamics

High School Biology

  • Absorption and Movement of Water in Plants
  • Adolescent Issues
  • Anatomy of Flowering Plants
  • Animal Kingdom
  • Bacteria and Fungi-Friends and Foe
  • Biodiversity and Conservation
  • Biofertilizers
  • Biological Classification
  • Biomedical Engineering
  • Biomolecules
  • Biotechnology and its Applications
  • Biotic Community
  • Body Fluids and Circulation
  • Breathing and Exchange of Gases
  • Cell – Unit of Life
  • Cell Cycle and Cell Division
  • Cell Division and Structure of Chromosomes
  • Cell Reproduction
  • Cellular Respiration
  • Chemical Coordination and Integration
  • Circulation
  • Control And Coordination
  • Crop Improvement
  • Digestion and Absorption
  • Diversity In Living Organisms
  • Ecosystem
  • Environmental Issues
  • Excretory Products and their Elimination
  • Flowering Plants
  • Genes and Chromosomes
  • Health and Diseases
  • Health and Its Significance
  • Heredity And Evolution
  • Heredity and Variation
  • How Do Organisms Reproduce?
  • Human Diseases
  • Human Eye And Colourful World
  • Human Health and Disease
  • Human Population
  • Human Reproduction
  • Hygiene
  • Improvement In Food Resources
  • Integumentary System- Skin
  • Kingdom Fungi
  • Kingdom Monera
  • Kingdom Protista
  • Life Processes
  • Locomotion and Movement
  • Microbes in Human Welfare
  • Mineral Nutrition
  • Molecular Basis of Inheritance
  • Morphology of Flowering Plants
  • Neural Control And Coordination
  • Nutrition in Human Beings
  • Organism and Population
  • Photosynthesis
  • Photosynthesis in Higher Plants
  • Plant Growth and Development
  • Plant Kingdom
  • Pollination and Fertilization
  • Pollution; Sources and its effects
  • Principles of Inheritance and Variation
  • Reproduction and Development in Angiosperms
  • Reproduction in Organisms
  • Reproductive Health
  • Respiration in Human Beings
  • Respiration in Plants
  • Respiratory System
  • Sexual Reproduction in Flowering Plants
  • Strategies for Enhancement in Food Production
  • Structural Organisation in Animals
  • Structural Organisation of the Cell
  • The Endocrine System
  • The Fundamental Unit Of Life
  • The Living World
  • The Nervous System and Sense Organs
  • Tissues
  • Transpiration
  • Transport in Plants

High School Math

  • Algebra – Arithmatic Progressions
  • Algebra – Complex Numbers and Quadratic Equations
  • Algebra – Linear Inequalities
  • Algebra – Pair of Linear Equations in Two Variables
  • Algebra – Polynomials
  • Algebra – Principle of Mathematical Induction
  • Algebra – Quadratic Equations
  • Binomial Theorem
  • Calculus – Applications of Derivatives
  • Calculus – Applications of the Integrals
  • Calculus – Continuity and Differentiability
  • Calculus – Differential Equations
  • Calculus – Integrals
  • Geometry – Area
  • Geometry – Circles
  • Geometry – Conic Sections
  • Geometry – Constructions
  • Geometry – Introduction to Euclid’s Geometry
  • Geometry – Three-dimensional Geometry
  • Geometry – Lines and Angles
  • Geometry – Quadrilaterals
  • Geometry – Straight Lines
  • Geometry – Triangles
  • Linear Programming
  • Matrices and Determinants
  • Mensuration – Areas
  • Mensuration – Surface Areas and Volumes
  • Number Systems
  • Number Systems – Real Numbers
  • Permutations and Combinations
  • Probability
  • Sequence and Series
  • Sets and Functions
  • Statistics 
  • Trignometry – Height and Distance
  • Trignometry – Identities
  • Trignometry – Introduction

Middle School Science

  • Acids, Bases And Salts
  • Air and Its Constituents
  • Basic Biology
  • Body Movements
  • Carbon and Its Compounds
  • Cell – Structure And Functions
  • Changes Around Us
  • Chemical Effects Of Electric Current
  • Chemistry in Your Life
  • Coal And Petroleum
  • Combustion And Flame
  • Components Of Food
  • Conservation Of Plants And Animals
  • Crop Production And Management
  • Electric Current And Its Effects
  • Electricity And Circuits
  • Elements and Compounds
  • Fibre To Fabric
  • Food production and management
  • Force And Pressure
  • Forests: Our Lifeline
  • Friction
  • Fun With Magnets
  • Garbage In, Garbage Out
  • Getting To Know Plants
  • Health and Hygiene
  • Heat
  • Hydrogen
  • Life Processes: Nutrition in Animals and Plants
  • Light, Shadows And Reflections
  • Materials: Metals And Non-Metals
  • Matter and Its States
  • Metals and Non-metals
  • Micro Organisms: Friend And Foe
  • Motion And Measurement Of Distances
  • Motion And Time
  • Nutrition In Animals
  • Nutrition In Plants
  • Organization in Living Things
  • Our Environment
  • Physical And Chemical Changes
  • Pollution and conservation
  • Pollution Of Air And Water
  • Reaching The Age Of Adolescence
  • Reproduction In Animals
  • Reproduction In Plants
  • Respiration In Organisms
  • Rocks and Minerals
  • Separation Of Substances
  • Simple Machines
  • Soil
  • Some Natural Phenomena
  • Sorting Materials Into Groups
  • Sound
  • Stars And The Solar System
  • Structure of Atom
  • Synthetic Fibers And Plastics
  • The Living Organisms And Their Surroundings
  • Transfer of Heat
  • Transformation of Substances
  • Transportation In Animals And Plants
  • Universe
  • Waste-water Story
  • Water: A Precious Resource
  • Weather, Climate And Adaptations Of Animals To Climate
  • Winds, Storms And Cyclones

Middle School Math

  • Addition
  • Area and Its Boundary
  • Boxes and Sketches
  • Data Handling
  • Fun With Numbers
  • Heavy and Light
  • How Many
  • Long And Short
  • Mapping
  • Measurement
  • Money
  • Multiplication and Factors
  • Multiply and Divide
  • Numbers
  • Parts and Wholes
  • Pattern Recognition
  • Patterns
  • Play With Patterns
  • Rupees And Paise
  • Shapes And Angles
  • Shapes And Designs
  • Shapes and Space
  • Similarity
  • Smart Charts
  • Squares
  • Subtraction
  • Tables And Shares
  • Tenths and Hundredths
  • Time
Please switch to portrait mode
for the best experience.
Click to open Popup