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# CBSE - Class 08 - Mathematics - Factorisation - NCERT Solutions

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# NCERT solutions for class 8 Mathematics Factorisation

## NCERT Class 8 Mathematics Chapter-wise Solutions

• Chapter 1 Rational Numbers
• Chapter 2 Linear Equations in One Variable
• Chapter 4 Practical Geometry
• Chapter 5 Data Handling
• Chapter 6 Squares and Square Roots
• Chapter 7 Cubes and Cube Roots
• Chapter 8 Comparing Quantities
• Chapter 9 Algebraic Expressions and Identities
• Chapter 10 Visualising Solid Shapes
• Chapter 11 Mensuration
• Chapter 12 Exponents and Powers
• Chapter 13 Direct and Inverse Proportions
• Chapter 14 Factorisation
• Chapter 15 Introduction to Graphs
• Chapter 16 Playing with Numbers

CBSE class 8th Mathematics have one books. Book has chapters and topics.

1. NCERT Mathematics Book Class 8

Here is the list of topics covered under each chapter of class 8 Mathematics NCERT text book.

• Exercise 1.1
• Exercise 1.2

• Exercise 2.1
• Exercise 2.2
• Exercise 2.3
• Exercise 2.4
• Exercise 2.5
• Exercise 2.6

• Exercise 3.1
• Exercise 3.2
• Exercise 3.3
• Exercise 3.4

• Exercise 4.1
• Exercise 4.2
• Exercise 4.3
• Exercise 4.4
• Exercise 4.5

• Exercise 5.1
• Exercise 5.2
• Exercise 5.3

• Exercise 6.1
• Exercise 6.2
• Exercise 6.3
• Exercise 6.4

• Exercise 7.1
• Exercise 7.2

• Exercise 8.1
• Exercise 8.2
• Exercise 8.3

• Exercise 9.1
• Exercise 9.2
• Exercise 9.3
• Exercise 9.4
• Exercise 9.5

### 10. Visualising Solid Shapes

• Exercise 10.1
• Exercise 10.2
• Exercise 10.3

### 11. Mensuration

• Exercise 11.1
• Exercise 11.2
• Exercise 11.3
• Exercise 11.4

### 12. Exponents and Powers

• Exercise 12.1
• Exercise 12.2

### 13. Direct and Inverse Proportions

• Exercise 13.1
• Exercise 13.2

### 14. Factorisation

• Exercise 14.1
• Exercise 14.2
• Exercise 14.3
• Exercise 14.4

### 15. Introduction to Graphs

• Exercise 15.1
• Exercise 15.2
• Exercise 15.3

### 16. Playing with Numbers

• Exercise 16.1
• Exercise 16.2

## NCERT Solution Chapter 14: Factorisation

Factorization (also factorisation in some forms of British English) or factoring is the decomposition of a mathematical object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained.

The aim of factoring is usually to reduce something to “basic building blocks” that cannot be further factored, such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viète's formulas relate the coefficients of a polynomial to its roots, which appear in the polynomial's factors.

The opposite of integer factorization is integer multiplication to obtain a product. The opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms.

Integer factorization for large integers appears to be a difficult problem. There is no known method to carry it out quickly, and its complexity is the basis of the assumed security of some public key cryptography algorithms, such as RSA.

A matrix can also be factorized into a product of matrices of special types, for an application in which that form is convenient. One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types: QR decomposition, LQ, QL, RQ, RZ.

Another example is the factorization of a function as the composition of other functions having certain properties; for example, every function can be viewed as the composition of a surjective function with an injective function. This situation is generalized by factorization systems.

## NCERT Solutions for Class 8th Mathematics

NCERT Solutions Class 8 Mathematics PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 8 Mathematics includes text book solutions. NCERT Solutions for CBSE Class 8 Mathematics have total 16 chapters. Class 8 Mathematics ncert Solutions in pdf for free Download are given in this website. Ncert Mathematics class 8 solutions PDF and Mathematics ncert class 8 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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