RBSE Maths Chapter 10 – Factorization Class 8 Important questions and solutions can be used as a reference to face the board examination. All the important questions, additional questions and solutions covering all the concepts of Chapter 10, available at BYJU’S, contain step by step answers. All these important questions are based on the new pattern designed by the RBSE. Students can also get the syllabus and textbooks on RBSE Class 8 solutions.

Chapter 10 of the RBSE Class 8 Maths will help the students to solve problems related to factors, factors of algebraic expressions, method of factorization, method of common factors, factorization by regrouping terms, factorization using identities, division of algebraic expressions.

### RBSE Maths Chapter 10: Exercise 10.1 Textbook Important Questions and Solutions

**Question 1: Find the common factors of the given terms.**

**[i] 12x, 36**

**[ii] 14pq, 28p ^{2}q^{2}**

**[iii] 6abc, 24ab ^{2}, 12a^{2}b**

**[iv] 16x ^{3}, -4x^{2}, 32x**

**[v] 10pq, 20qr, 30rp**

**[vi] 3x ^{2}y^{3}, 10x^{2}y^{2}, 6x^{2}y^{2}z**

**Solution: **

**[i] 12x, 36**

12x = 2 * 2 * 3 * x

36 = 2 * 2 * 3 * 3

The common factors of 12x and 36 are 2 * 2 * 3 = 12

**[ii] 14pq, 28p ^{2}q^{2}**

14pq = 2 * 7 * p * q

28p^{2}q^{2} = 2 * 7 * 2 * p * p * q * q

The common factors of 14pq, 28p^{2}q^{2} are 2 * 7 * p * q = 14pq

**[iii] 6abc, 24ab ^{2}, 12a^{2}b**

6abc = 2 * 3 * a * b * c

24ab^{2} = 2 * 2 * 2 * 3 * a * b * b

12a^{2}b = 2 * 2 * 3 * a * a * b

The common factors of 6abc, 24ab^{2}, 12a^{2}b are 2 * 3 * a * b = 6ab

**[iv] 16x ^{3}, -4x^{2}, 32x**

16x^{3} = 2 * 2 * 2 * 2 * x * x * x

-4x^{2} = (-1) * 2 * 2 * x * x

32x = 2 * 2 * 2 * 2 * 2 * x

The common factors of 16x^{3}, -4x^{2}, 32x are 2 * 2 * x = 4x

**[v] 10pq, 20qr, 30rp**

10pq = 2 * 5 * p * q

20qr = 2 * 5 * 2 * q * r

30rp = 2 * 3 * 5 * r * p

The common factors of 10pq, 20qr, 30rp are 2 * 5 = 10

**[vi] 3x ^{2}y^{3}, 10x^{2}y^{2}, 6x^{2}y^{2}z**

3x^{2}y^{3 }= 3 * x * x * y * y * y

10x^{2}y^{2} = 2 * 5 * x * x * y * y

6x^{2}y^{2}z = 2 * 3 * x * x * y * y * z

The common factors of 3x^{2}y^{3}, 10x^{2}y^{2}, 6x^{2}y^{2}z are x * x * y * y = x^{2}y^{2}

**Question 2: Factorise the following expressions by common factors method.**

**[i] 6p – 12q**

**[ii] 7a ^{2} + 14a**

**[iii] 10a ^{2} – 15b^{2} + 20c^{2}**

**[iv] ax ^{2}y + bxy^{2} + cxyz**

**[v] x ^{2}yz + xy^{2}z + xyz^{2}**

**[vi] -16z + 20z ^{3}**

**Solution:**

**[i] 6p – 12q**

6 is taken commonly from the terms,

= 6 (p – 2q)

**[ii] 7a ^{2} + 14a**

7a is taken commonly from the terms,

= 7a (a + 2)

**[iii] 10a ^{2} – 15b^{2} + 20c^{2}**

5 is taken commonly from the terms,

= 5 (2a^{2} – 3b^{2} + 4c^{2})

**[iv] ax ^{2}y + bxy^{2} + cxyz**

xy is taken commonly from the terms,

= xy (ax + by + cz)

**[v] x ^{2}yz + xy^{2}z + xyz^{2}**

xyz is taken commonly from the terms,

= xyz (x + y + z)

**[vi] -16z + 20z ^{3}**

= (4z) (-4 + 5z^{2})

**Question 3:** **Factorise the following expressions by regrouping method.**

**[i] 2xy + 3 + 2y + 3x**

**[ii] z – 7 – 7xy + xyz**

**[iii] 6xy – 4y + 6 – 9x**

**[iv] 15pq + 15 + 9q + 25p**

**Solution: **

**[i] 2xy + 3 + 2y + 3x**

= 2xy + 2y + 3 + 3x

= 2y (x + 1) + 3 ( 1 + x)

= (2y + 3) (x + 1)

**[ii] z – 7 – 7xy + xyz**

= z – 7 – xy (7 – z)

= 1 (z – 7) + xy ( z – 7)

= (1 + xy) (z – 7)

**[iii] 6xy – 4y + 6 – 9x**

= 2y (3x – 2) – 3 (-2 + 3x)

= (2y – 3) (3x – 2)

**[iv] 15pq + 15 + 9q + 25p**

= 15pq + 9q + 15 + 25p

= 3q (5p + 3) + 5 (3 + 5p)

= (3q + 5) (3 + 5p)

### RBSE Maths Chapter 10: Exercise 10.2 Textbook Important Questions and Solutions

**Question 1: Factorize the following expressions.**

**[i] a ^{2} – 4**

**[ii] a ^{2} – 49b^{2}**

**[iii] p ^{3} – 121p**

**[iv] (a – b) ^{2} – c^{2}**

**[v] a ^{4} – b^{4}**

**[vi] 5x ^{3} – 125x**

**[vii] 63a ^{2} – 112b^{2}**

**[viii] 9x ^{2}y^{2} – 16**

**[ix] (l + m) ^{2} – (l – m)^{2}**

**Solution:**

**Question 2: Factorise the following expressions.**

**[i] lx ^{2} + mx**

**[ii] 2x ^{3} + 2xy^{2} + 2xz^{2}**

**[iii] a (a + b) + 4 (a + b)**

**[iv] (xy + y) + x + 1**

**[v] 5a ^{2} – 15a – 6c + 2ac**

**[vi] am ^{2} + bm^{2} + bn^{2} + an^{2}**

**Solution:**

**Question 3: Factorise the following expressions.**

**[i] x ^{2} + 5x + 6**

**[ii] q ^{2} + 11q + 24**

**[iii] m ^{2} – 10m + 21**

**[iv] x ^{2} + 6x – 16**

**[v] x ^{2} – 7x – 18**

**[vi] k ^{2} – 11k – 102**

**[vii] y ^{2} + 2y – 48**

**[viii] d ^{2} – 4d – 45**

**[ix] m ^{2} + 16m + 63**

**[x] n ^{2} – 19n – 92**

**[xi] p ^{2} – 10p + 16**

**[xii] x ^{2} + 4x – 45**

**Solution:**

### RBSE Maths Chapter 10: Exercise 10.3 Textbook Important Questions and Solutions

**Question 1: Carry out the following divisions.**

**[i] 28x ^{4 }÷ 56x**

**[ii] -36y ^{3} ÷ 9y^{2}**

Solution:

**Question 2: Divide the given polynomial by the given monomial**

**[i] (5x ^{2} – 6x) by 3x**

**[ii] (x ^{3} + 2x^{2} + 3x) by 2x**

**Solution:**

**Question 3: Solve the following.**

**[i] 10y (6y + 21) ÷ 5(2y + 7)**

**[ii] 9x ^{2}y^{2} (3z – 24) ÷ 27xy (z – 8)**

**Solution: **

**Question 4: Factorise the given expressions and divide them as directed.**

**[i] (y ^{2} + 7y + 10) ÷ (y + 5)**

**[ii] (5x ^{2} – 25x + 20) ÷ ( x – 1)**

**Solution: **