linear polynomial Archives – Mathemafia

Class 10 – Chapter 2 – Polynomials – Last Minute Formula Revision

Sunil Kumar — Sun, 02 Feb 2025 09:06:02 +0000

⏰ Last minute Formula Revision 🔥 Polynomials, Chapter 2, Class 10

This short video covers all the formulas of chapter 2 (Polynomials) of class 10. It is recommended to watch this before your exam to quickly recall all the formulas of this chapter.

The tutorial is available in Hinglish + 9 different languages: English, French, German, Hindi, Spanish, Indonesian, Italian, Japanese, Portuguese

The post Class 10 – Chapter 2 – Polynomials – Last Minute Formula Revision appeared first on Mathemafia.

Class 10 | Chapter 2 | All Solutions | Polynomials

Sunil Syal — Fri, 17 Dec 2021 07:37:47 +0000

This playlist covers all the questions, concepts and examples of chapter 2 (Polynomials) of class 10, NCERT book. Click a thumbnail to watch the tutorial.

Watch complete chapter on YouTube

Example 1 – Chapter 2 – Class 10, Maths | Polynomials | NCERT Maths | CBSE

Example 2 – Chapter 2 – Class 10, Maths | Polynomials | NCERT Maths | CBSE

Example 3 – Chapter 2 – Class 10, Maths | Polynomials | NCERT Maths | CBSE

Example 4 – Chapter 2 – Class 10, Maths | Polynomials | NCERT Maths | CBSE

Example 5* – Chapter 2 – Class 10, Maths | Polynomials | NCERT Maths | CBSE

The post Class 10 | Chapter 2 | All Solutions | Polynomials appeared first on Mathemafia.

Class 10 | Chapter 2 | Polynomials | Exercise 2.1

Sunil Syal — Sun, 20 Jun 2021 04:41:12 +0000

Question 1: The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

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❇️ ❇️ M️aster List – All Maths Formulas, Class 10 ❇️ ❇️

🇮🇳 हर भारतीय के दिल की आवाज़… आइए, इस स्वतंत्रता दिवस मिलकर गाएँ – “भारत माता की जय“।

Class 10 – Mathematics – NCERT Solutions

Real Numbers
- Exercise 1.1
- Exercise 1.2
Polynomials
- Exercise 2.1
- Exercise 2.2
Pair of Linear Equation in Two Variables

Quadratic Equations
Arithmetic Progressions
- Exercise 5.1
- Exercise 5.2
Triangles
- Exercise 6.1
- Exercise 6.2
- Exercise 6.3

Coordinate Geometry
- Exercise 7.1
- Exercise 7.2
Introduction to Trigonometry
Some Applications of Trigonometry
- Exercise 9.1
Circles
- Exercise 10.1
- Exercise 10.2

Areas Related to Circles
- Exercise 11.1
Surface Areas and Volumes
- Exercise 12.1
- Exercise 12.2
Statistics
- Exercise 13.1
- Exercise 13.2
- Exercise 13.3
Probability
- Exercise 14.1

Super Cool Stuff

Calculators
- Quadratic Equation Calculator – Solve any Equation
Super Concepts

Theorems
Quizzes

The post Class 10 | Chapter 2 | Polynomials | Exercise 2.1 appeared first on Mathemafia.

Class 10 | Chapter 2 | Polynomials | Exercise 2.3

Sunil Syal — Sun, 20 Jun 2021 03:19:37 +0000

Question 1: Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following :
(i) p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2
(ii) p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 – x
(iii) p(x) = x4 – 5x + 6, g(x) = 2 – x2

Question 2: Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: (i) t2 – 3 , 2t4 + 3t3 – 2t2 – 9t – 12
(ii) x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2 (iii) x3 – 3x + 1, x5 – 4x3 + x2 + 3x + 1

Question 3: Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are 5/3 and – 5/3⋅

Question 4: On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x).

Question 5: Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and
(i) deg p(x) = deg q(x) (ii) deg q(x) = deg r(x) (iii) deg r(x) = 0

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🇮🇳 हर भारतीय के दिल की आवाज़… आइए, इस स्वतंत्रता दिवस मिलकर गाएँ – “भारत माता की जय“।

Class 10 – Mathematics – NCERT Solutions

Real Numbers
- Exercise 1.1
- Exercise 1.2
Polynomials
- Exercise 2.1
- Exercise 2.2
Pair of Linear Equation in Two Variables

Quadratic Equations
Arithmetic Progressions
- Exercise 5.1
- Exercise 5.2
Triangles
- Exercise 6.1
- Exercise 6.2
- Exercise 6.3

Coordinate Geometry
- Exercise 7.1
- Exercise 7.2
Introduction to Trigonometry
Some Applications of Trigonometry
- Exercise 9.1
Circles
- Exercise 10.1
- Exercise 10.2

Areas Related to Circles
- Exercise 11.1
Surface Areas and Volumes
- Exercise 12.1
- Exercise 12.2
Statistics
- Exercise 13.1
- Exercise 13.2
- Exercise 13.3
Probability
- Exercise 14.1

Super Cool Stuff

Calculators
- Quadratic Equation Calculator – Solve any Equation
Super Concepts

Theorems
Quizzes

The post Class 10 | Chapter 2 | Polynomials | Exercise 2.3 appeared first on Mathemafia.

Class 10 | Chapter 2 | Polynomials | Exercise 2.2

Sunil Syal — Sun, 20 Jun 2021 03:19:13 +0000

Question 1: Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x² –2x–8 (ii) 4s² –4s+1 (iii) 6x² –3–7x (iv) 4u² +8u (v) t2 –15 (vi) 3x² –x–4

Question 2: Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

i) 1/4,−1 (ii) √2, 1/3 (iii) 0, √5 (iv) 1,1 (v) − 1/4, 1/4 (vi) 4,1

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– Saiba’s Parents (USA)

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❇️ ❇️ M️aster List – All Maths Formulas, Class 10 ❇️ ❇️

🇮🇳 हर भारतीय के दिल की आवाज़… आइए, इस स्वतंत्रता दिवस मिलकर गाएँ – “भारत माता की जय“।

Class 10 – Mathematics – NCERT Solutions

Real Numbers
- Exercise 1.1
- Exercise 1.2
Polynomials
- Exercise 2.1
- Exercise 2.2
Pair of Linear Equation in Two Variables

Quadratic Equations
Arithmetic Progressions
- Exercise 5.1
- Exercise 5.2
Triangles
- Exercise 6.1
- Exercise 6.2
- Exercise 6.3

Coordinate Geometry
- Exercise 7.1
- Exercise 7.2
Introduction to Trigonometry
Some Applications of Trigonometry
- Exercise 9.1
Circles
- Exercise 10.1
- Exercise 10.2

Areas Related to Circles
- Exercise 11.1
Surface Areas and Volumes
- Exercise 12.1
- Exercise 12.2
Statistics
- Exercise 13.1
- Exercise 13.2
- Exercise 13.3
Probability
- Exercise 14.1

Super Cool Stuff

Calculators
- Quadratic Equation Calculator – Solve any Equation
Super Concepts

Theorems
Quizzes

The post Class 10 | Chapter 2 | Polynomials | Exercise 2.2 appeared first on Mathemafia.

Class 10 | Chapter 2 | Polynomials | Examples

Sunil Syal — Sun, 20 Jun 2021 03:13:40 +0000

Example 1: Look at the graphs in Fig. 2.9 given below. Each is the graph of y = p(x), where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x).

Example 2: Find the zeroes of the quadratic polynomial x² + 7x + 10, and verify the relationship between the zeroes and the coefficients.

Example 3: Find the zeroes of the polynomial x² – 3 and verify the relationship between the zeroes and the coefficients.

Example 4: Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2, respectively.

Example 5: Verify that 3, –1, −1/3 are the zeroes of the cubic polynomial p(x) = 3x³ – 5x² – 11x – 3, and then verify the relationship between the zeroes and the coefficients.

Example 6: Divide 2x² +3x+1 by x+2.

Example 7: Divide 3x³ +x2 +2x+5 by 1+2x+x2.

Example 8: Divide 3x² – x³ – 3x + 5 by x – 1 – x², and verify the division algorithm.

Example 9: Find all the zeroes of 2x⁴ –3x³ –3x² +6x–2, if you know that two of its zeroes are 2 and − 2.

Testimonials

An Excellent Math Teacher

– Saiba’s Parents (USA)

Amazing Math Coach

– Rishi’s Parents (USA)

Unique, Patient and Good Mentor

Also, your videos on Mathemafia youtube channel are very informative.

– Lakshay (USA)

WhatsApp for 1-1 Classes

❇️ ❇️ M️aster List – All Maths Formulas, Class 10 ❇️ ❇️

🇮🇳 हर भारतीय के दिल की आवाज़… आइए, इस स्वतंत्रता दिवस मिलकर गाएँ – “भारत माता की जय“।

Class 10 – Mathematics – NCERT Solutions

Real Numbers
- Exercise 1.1
- Exercise 1.2
Polynomials
- Exercise 2.1
- Exercise 2.2
Pair of Linear Equation in Two Variables

Quadratic Equations
Arithmetic Progressions
- Exercise 5.1
- Exercise 5.2
Triangles
- Exercise 6.1
- Exercise 6.2
- Exercise 6.3

Coordinate Geometry
- Exercise 7.1
- Exercise 7.2
Introduction to Trigonometry
Some Applications of Trigonometry
- Exercise 9.1
Circles
- Exercise 10.1
- Exercise 10.2

Areas Related to Circles
- Exercise 11.1
Surface Areas and Volumes
- Exercise 12.1
- Exercise 12.2
Statistics
- Exercise 13.1
- Exercise 13.2
- Exercise 13.3
Probability
- Exercise 14.1

Super Cool Stuff

Calculators
- Quadratic Equation Calculator – Solve any Equation
Super Concepts

Theorems
Quizzes

The post Class 10 | Chapter 2 | Polynomials | Examples appeared first on Mathemafia.

Class 9 | Chapter 2 | Polynomials | Exercise 2.4 | Question 5

Sunil Syal — Mon, 21 Sep 2020 14:24:44 +0000

Question 5: Factorise : (i) x³ – 2x² – x + 2 (ii) x³ – 3x² – 9x – 5 (iii) x³ + 13x² + 32x + 20 (iv) 2y³ + y² – 2y – 1

Prerequisite

Factorising a cubic polynomial seems tricky and difficult but believe me, it is not at all difficult. All you need to know is about the possible rational zeros / roots of a polynomial / equation. You can try to find the value of p(x) for these possible values. Once you get such a number, a, for which p(a) is zero, (x-a) will be a factor of the polynomial (by factor theorem). After that we must use splitting the middle term method to find the rest of the polynomials.

Steps:

Find probable rational roots by using the rational root theorem. No need to worry about this theorem. It has been explained in detail in this tutorial.
Find the value of p(x) for these rational numbers. If you get a number, a, for which p(a) is zero, (x-a) will be one factor.
Divide p(x) by (x-a) and get the quotient (quadratic polynomial).
Factorise the quotient using splitting the middle term method.

Chapter 2 – Polynomials

Here you will find complete solution of all questions, concepts, theorems and examples of class 9 chapter 2 (Polynomials) of class 9, NCERT textbook.

There are few very important concepts that students must learn to get a good understanding of polynomials:

All above mentioned tutorials are included in the list displayed below for class 9 chapter 2 (Polynomials). You are strongly advised to watch all these videos thoroughly and do not miss any of these if you really want to get good hold on polynomials.

Click a thumbnail to watch the tutorial.

Watch complete chapter on YouTube

Introduction to Polynomials | Introduction to Algebra | Class 9, Chapter 2, NCERT Maths

Class 9 | Chapter 2 | Polynomials Example 1 | Finding Degree | NCERT Maths

Question 1 Exercise 2.1 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 2 Exercise 2.1 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 3 Exercise 2.1 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 4 Exercise 2.1 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 5 Exercise 2.1 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Class 9 | Chapter 2 | Polynomials Example 2 explained | NCERT Maths

Class 9 | Chapter 2 | Polynomials Example 3 explained | NCERT Maths

Class 9 | Chapter 2 | Polynomials Example 4 explained | NCERT Maths

Class 9 | Chapter 2 | Polynomials Example 5 explained | NCERT Maths

Question 1 Exercise 2.2 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 2 Exercise 2.2 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 3 Exercise 2.2 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 4 Exercise 2.2 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

FACTOR THEOREM Proof Explained | Class 9 | Chapter 2 | Polynomials, 2.5 Factorisation of Polynomials

Example 6 Chapter 2 Class 9 | Polynomials, Factor Theorem Questions | NCERT Maths

Example 7 Chapter 2 Class 9 | Polynomials, Factor Theorem Questions | NCERT Maths

Factorisation of Polynomials by SPLITTING THE MIDDLE TERM Explained| Class 9 |Chapter 2| NCERT Maths

Example 8 Chapter 2 Class 9 | Polynomials | 1St Solution | Splitting Middle Term Questions | Maths

Example 8 Chapter 2 Class 9 | Polynomials | 2nd Solution | Factor Theorem Questions |NCERT Maths

Example 9 Chapter 2 Class 9 | Polynomials | Factorise using Factor Theorem Questions |NCERT Maths

Example 10 Chapter 2 Class 9 | Polynomials | Factorise cubic or degree 3 polynomials | NCERT Maths

Question 1 Exercise 2.3 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 2 Exercise 2.3 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 3 Exercise 2.3 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 4 Exercise 2.3 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 5 Exercise 2.3 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

EASY TIPS & TRICKS 🔥 TO LEARN ALGEBRAIC IDENTITIES | Class 9 | Chapter 2 | Polynomials | NCERT Maths

Example 11 Chapter 2 Class 9 | Polynomials | Product of polynomials using algebraic identities

Example 12 Chapter 2 Class 9 | Polynomials| Example 17 |Product of big numbers without multiplying

Example 13 Chapter 2 Class 9 | Polynomials | Factorise polynomials using algebra identities | NCERT

Example 14 Chapter 2 Class 9 | Polynomials | Expand polynomials using algebraic identities | NCERT

Example 15 Chapter 2 Class 9 | Polynomials | How to expand polynomials using algebraic formulae |

Example 16 Chapter 2 Class 9 | Polynomials | Factorise polynomials using algebraic identities

Example 17 Chapter 2 Class 9 | Polynomials | How to expand polynomials using algebraic formulae

Example 18 Chapter 2 Class 9 | Polynomials | Example 23 | Cubes of big numbers without multiplying

Example 19 Chapter 2 Class 9 | Polynomials |Factorise cubic polynomials using algebraic identities

Example 20 Chapter 2 Class 9 | Polynomials | Factorise cubic polynomials using algebraic identities

Question 1 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 2 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 3 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 4 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 5 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 6 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 7 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 8 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 9 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 10 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Question 11 Exercise 2.4 Class 9 | Chapter 2 (Polynomials) | NCERT Maths | Solution

Class 9 Chapter 3 | Coordinate Geometry

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Class 9 | Chapter 2 | Polynomials | Exercise 2.4 | Question 4

Sunil Syal — Mon, 21 Sep 2020 14:24:40 +0000

Question 4: Factorise : (i) 12x² – 7x + 1 (ii) 2x² + 7x + 3 (iii) 6x² + 5x – 6 (iv) 3x² – x – 4

Prerequisite

Factorisation of a 2 degree polynomial (quadratic polynomial) is one of the easiest things to do in this chapter. If you are not asked to use a specific method to factorise a quadratic polynomial, it is always recommended to use splitting the middle term method.

Factorise by splitting the middle term