OP Malhotra Factorisation Class-9 S.Chand ICSE Maths Ch-4

OP Malhotra Factorisation Class-9 S.Chand ICSE Maths Ch-4. We Provide Step by Step Answer of Exe-4(a), Exe-4(b), Exe-4(c), Exe-4(d), Exe-4(e), Exe-4(f), Exe-4(g), Exe-4(h), with Chapter Test of S Chand OP Malhotra Maths . Visit official Website CISCE  for detail information about ICSE Board Class-9.

OP Malhotra Factorisation Class-9 S.Chand ICSE Maths Ch-4

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-: Select Topics :-

Exercise-4(a)

Exercise-4(b)

Exercise-4(c)

Exercise-4(d)

Exercise-4(e)

Exercise-4(f)

Exercise-4(g)

Exercise-4(h)

Chapter Test

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Exercise-4

OP Malhotra Factorisation Class-9 S.Chand ICSE Maths Ch-4

Factorisation :

Factorisation or factoring is the decomposition of an 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 x^2 − 4 factors as (x − 2) (x + 2).
In all cases, a product of simpler objects is obtained. It is actually the opposite of expansion.

Methods of factorization:

1. Taking out the common factors.
2. Grouping
3. Splitting of the middle terms.
4. Difference of two squares.
5. The sum or difference of two cubes.

If a given polynomial contains a common factor which may be either a constant or a variable, we divide each term of the polynomial by that common factor and enclose the quotient within the brackets keeping the common factor outside the bracket
For example,

3𝑎² − 6𝑎²𝑏 − 12𝑎𝑏²
= 3𝑎 (𝑎² − 2𝑎𝑏 − 4𝑏²)
If the polynomial has even number of terms, then the terms are first arranged in groups such that each group has a common factor
For example, 𝑎² − 2𝑏 − 2𝑎 + 𝑎𝑏

= 𝑎² − 2𝑎 + 𝑎𝑏 − 2𝑏
= 𝑎(𝑎 − 2) + 𝑏(𝑎 − 2)
=(𝑎 + 𝑏)(𝑎 − 2)
If the polynomial is trinomial in nature, i.e., it has 3 terms, we first arrange the terms in descending order. There after split the middle term in such a way that their product is equal to the product of the first and the last term. For example,

𝑥² − 3𝑥 − 28
= 𝑥² − 7𝑥 + 4𝑥 − 28
= 𝑥(𝑥 − 7) + 4(𝑥 − 7)
= (𝑥 + 4)(𝑥 − 7)
If the polynomial is a difference of two squares then we use the identity:
𝑥² − 𝑦² = (𝑥 − 𝑦)(𝑥 + 𝑦)
For example, 16𝑥² − 49𝑦²
= (4𝑥)²−(7𝑦)²
= (4𝑥 − 7𝑦)(4𝑥 + 7𝑦)

Factors of Natural Numbers :

Factors are the pair of natural numbers which give the resultant number.

Example

24 = 12 × 2 = 6 × 4 = 8 × 3 = 2 × 2 × 2 × 3 = 24 × 1

Hence, 1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24.

Prime Factor Form :

If we write the factors of a number in such a way that all the factors are prime numbers then it is said to be a prime factor form.

Example

The prime factor form of 24 is

24 = 2 × 2 × 2 × 3

Factors of Algebraic Expressions :

Like any natural number, an algebraic expression is also the product of its factors. In the case of algebraic expression, it is said to be an irreducible form instead of prime factor form.

Example

7pq = 7 × p × q =7p × q = 7q × p = 7 × pq

These are the factors of 7pq but the irreducible form of it is

7pq = 7 × p × q

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Exercise-4.(a)

OP Malhotra Factorisation Class-9 S.Chand ICSE Maths Ch-4

Question 1:

8x + 16 y

Question 2:

ax – 2ay

Question 3:

……………………

……………………

………………………

Question 15:

(x – y)⁶ + (y – x)⁵

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Exercise-4.(b)

 Factorisation Class-9 S.Chand ICSE Maths Ch-4

Question 1:

bx + 2b + cx + 2c

Question 2:

y³ + 2y² + 3y + 6

Question 3:

…………………….

……………………..

……………………….

Question 12:

(p² + 1) q – p² – y²

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Exercise-4.(c)

OP Malhotra Factorisation Class-9 S.Chand ICSE Maths Ch-4

Question 1:

x² + 4x + 4

Question 2:

x² + 6x + 9

Question 3:

…………………..

…………………..

……………………

Question 8:

25p² + 5p/2q + 1/16q²

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Exercise-4.(d)

 Factorisation Class-9 S.Chand ICSE Maths Ch-4

Question 1:

x² – 4

Question 2:

y² – 25

Question 3:

…………………….

…………………….

…………………….

Question 14:

(3.2)² – (1.8)²

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Exercise-4.(e)

OP Malhotra Factorisation Class-9 S.Chand ICSE Maths Ch-4

Question 1:

7x² – 7

Question 2:

8 – 50 y² z²

Question 3:

……………………

……………………

……………………

Question 30:

(x² + 8x + 15) (x² – 8x + 15)

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Exercise-4.(f)

Factorisation Class-9 S.Chand ICSE Maths Ch-4

Question 1:

a² + 5a + 6

Question 2:

a² + 6a + 8

Question 3:

……………………

……………………

……………………

Question 20:

(x² + x)² + 4(x² + x) – 21

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Exercise-4.(g)

OP Malhotra Factorisation Class-9 S.Chand ICSE Maths Ch-4

Question 1:

2x² + 3x + 1

Question 2:

3x² + 17x + 10

Question 3:

………………………

………………………

……………………….

Question 16:

2(a + b)² – 5 (a + b) – 3

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Exercise-4.(h)

OP Malhotra Factorisation Class-9 S.Chand ICSE Maths Ch-4

Question 1:

a³ + 1

Question 2:

x³ + 8

Question 3:

8x³ + 1

Question 4:

………………………

……………………….

……………………….

Question 24:

a⁴  + b⁴ = a² b²

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Chapter Test

 Factorisation Class-9 S.Chand ICSE Maths Ch-4

Question 1:

8x²y³ – x⁵

Question 2:

……………………

…………………….

……………………

Question 10:

x – 2y = 11, xy = 8

— : End of Factorisation OP Malhotra S Chand Solutions :–

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Return to :–   OP Malhotra S Chand Solutions for ICSE Class-9 Maths

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