RD Sharma Solutions for Class 9 Maths Chapter 5 Factorization of Algebraic Expressions

Here are the RD Sharma Class 9 Maths Chapter 5 Solutions, designed to help students prepare effectively for their exams. By referring to these solutions and practicing the problems, students can boost their confidence and improve their scores.

RD Sharma Solution for Class 9 Chapter 5 - Question with Answer

RD Sharma Solutions for Class 9 Maths Chapter 5 - Factorization of Algebraic Expressions, divided into exercises:

Exercise 5.1: Factorization Using Common Factors

1. Question: Factorize: 6x + 9
   Solution:
   First, identify the common factor of both terms (6x and 9). The greatest common factor (GCF) is 3.
   Factor out 3 from both terms:
   6x + 9 = 3(2x + 3).
2. Question: Factorize: 12a + 15b
   Solution:
   The GCF of 12a and 15b is 3.
   Factor out 3:
   12a + 15b = 3(4a + 5b).
3. Question: Factorize: 14x + 21
   Solution:
   The GCF of 14x and 21 is 7.
   Factor out 7:
   14x + 21 = 7(2x + 3).
4. Question: Factorize: 10y + 5z
   Solution:
   The GCF of 10y and 5z is 5.
   Factor out 5:
   10y + 5z = 5(2y + z).
5. Question: Factorize: 18p + 24q
   Solution:
   The GCF of 18p and 24q is 6.
   Factor out 6:
   18p + 24q = 6(3p + 4q).

Exercise 5.2: Factorization Using the Grouping Method

1. Question: Factorize: 3xy + 2x + 3y + 2
   Solution:
   Group terms:
   (3xy + 3y) + (2x + 2)
   Factor out the common factors from each group:
   3y(x + 1) + 2(x + 1)
   Now, factor out (x + 1):
   (x + 1)(3y + 2).
2. Question: Factorize: x² + 5x + 2x + 10
   Solution:
   Group terms:
   (x² + 5x) + (2x + 10)
   Factor out the common factors from each group:
   x(x + 5) + 2(x + 5)
   Now, factor out (x + 5):
   (x + 5)(x + 2).
3. Question: Factorize: ab + ac + bc + c
   Solution:
   Group terms:
   (ab + ac) + (bc + c)
   Factor out the common factors from each group:
   a(b + c) + c(b + c)
   Now, factor out (b + c):
   (b + c)(a + c).
4. Question: Factorize: x² + 3x + 2x + 6
   Solution:
   Group terms:
   (x² + 3x) + (2x + 6)
   Factor out the common factors from each group:
   x(x + 3) + 2(x + 3)
   Now, factor out (x + 3):
   (x + 3)(x + 2).
5. Question: Factorize: pq + pr + qr + r
   Solution:
   Group terms:
   (pq + pr) + (qr + r)
   Factor out the common factors from each group:
   p(q + r) + r(q + r)
   Now, factor out (q + r):
   (q + r)(p + r).

Exercise 5.3: Factorization Using Algebraic Identities

1. Question: Factorize: x² + 6x + 9
   Solution:
   The given expression matches the form of (a + b)², where a = x and b = 3.
   So, x² + 6x + 9 = (x + 3)².
2. Question: Factorize: x² - 10x + 25
   Solution:
   The given expression matches the form of (a - b)², where a = x and b = 5.
   So, x² - 10x + 25 = (x - 5)².
3. Question: Factorize: a² + 4ab + 4b²
   Solution:
   The given expression matches the form of (a + b)², where a = a and b = 2b.
   So, a² + 4ab + 4b² = (a + 2b)².
4. Question: Factorize: x² - 16
   Solution:
   The given expression matches the form of (a + b)(a - b), where a = x and b = 4.
   So, x² - 16 = (x + 4)(x - 4).
5. Question: Factorize: m² - 9
   Solution:
   The given expression matches the form of (a + b)(a - b), where a = m and b = 3.
   So, m² - 9 = (m + 3)(m - 3).

Exercise 5.4: Factorization of Quadratic Polynomials

1. Question: Factorize: x² + 7x + 12
   Solution:
   We need two numbers that multiply to 12 and add to 7. These numbers are 3 and 4.
   So, x² + 7x + 12 = (x + 3)(x + 4).
2. Question: Factorize: x² - 5x + 6
   Solution:
   We need two numbers that multiply to 6 and add to -5. These numbers are -2 and -3.
   So, x² - 5x + 6 = (x - 2)(x - 3).
3. Question: Factorize: x² - 3x - 10
   Solution:
   We need two numbers that multiply to -10 and add to -3. These numbers are -5 and 2.
   So, x² - 3x - 10 = (x - 5)(x + 2).
4. Question: Factorize: x² + 8x + 15
   Solution:
   We need two numbers that multiply to 15 and add to 8. These numbers are 3 and 5.
   So, x² + 8x + 15 = (x + 3)(x + 5).
5. Question: Factorize: x² - 2x - 15
   Solution:
   We need two numbers that multiply to -15 and add to -2. These numbers are -5 and 3.
   So, x² - 2x - 15 = (x - 5)(x + 3).