remainder theorem Archives – 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