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

21 Sep
Class 9 - Polynomials, Math - Class 9 | NCERT, , , , , , , , , ,

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

Question 4
Ex: 2.5 | Question 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
Class 9 Chapter 3 | Coordinate Geometry
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Theorems / Concepts

Basics of polynomials

Remainder theorem

Factor theorem

Factorise – Splitting the middle term

Algebraic Identities

Exercise 2.1

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 2.2

Question 1

Question 2

Question 3

Question 4

Exercise 2.3

Question 1

Question 2

Question 3

Exercise 2.4

Question 1

Question 2

Question 3

Question 4

Question 5

Exercise 2.5

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Exercise 2.5

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Examples

Example 11

Example 12

Example 13

Example 14

Example 15

Example 16

Example 17

Example 18

Example 19

Example 20

Examples

Example 21

Example 22

Example 23

Example 24

Example 25

Good to learn

Rational root theorem

Synthetic division – Part 1

Synthetic division – Part 2

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