RBSE Solutions for Class 8 Maths Chapter 10 Factorization Additional Questions is part of RBSE Solutions for Class 8 Maths. Here we have given Rajasthan Board RBSE Class 8 Maths Chapter 10 Factorization Additional Questions.

Board |
RBSE |

Textbook |
SIERT, Rajasthan |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 10 |

Chapter Name |
Factorization |

Exercise |
Additional Questions |

Number of Questions |
39 |

Category |
RBSE Solutions |

## Rajasthan Board RBSE Class 8 Maths Chapter 10 Factorization Additional Questions

**I.Objective Type Questions**

Question 1.

Factors of expression x² + (a + b) x + ab are

(a) (x + a)(x – b)

(b) (x – a) (x + b)

(c) (x + a)(x + b)

(d) (x – a) (x – b)

Question 2.

Square of (2x + 3) is

(a) 4x² + 6x + 9

(b) 4x² + 2x + 9

(c) 4x² + 12x + 9

(d) 4x² + 9

Question 3.

Square of (6x + 1) is

(a) 36x² + 1

(b) 36x² + 6x + 1

(c) 36x² + 6

(d) 36x² + 12x + 1.

Question 4.

The product(RBSESolutions.com)of expression (2a – 3) (2a + 3) is

(a) 4a² + 2a + 9

(b) 4a² – 9

(c) 4a² – 6

(d) 4a² – 4a + 9

Question 5.

Common factor of 6x + 18xy is

(a) y

(b) 6y

(c) 6x

(d) xy

Question 6.

Factor of 2x³ + x² + 2x + 1 is

(a) (2x + 1)(x² + 1)

(b) (x² + 2)(x + 1)

(c) (x + 2)(x² + 1)

(d) (x² + 1)(x + 1)

Question 7.

Factor of 4x² + 8xy + 4y² is

(a) (2x + 2y)²

(b) (2x – 2y)²

(c) (2x + y)²

(d) (x + 2y)²

Question 8.

The factors(RBSESolutions.com)of expression a² + 2ab + b² are

(a) (a + b)(a – b)

(b) (a + b)²

(c) (a – b)²

(d) (a² + b²)²

Question 9.

The factors of expression a² – b² are

(a) (a² – b²)

(b) (a² – b²) (a + b)

(c) (a + b) (a + b)

(d) (a – b) (a + b)

Answers

1. (c)

2. (c)

3. (d)

4. (b)

5. (c)

6. (a)

7. (a)

8. (b)

9. (d).

**II. Fill in the blanks**

Question 1.

The equation which is true for all value of variables is called ___

Question 2.

(x + a) (x + b) = x² + (….) x + (ab)

Question 3.

a² – b² = (…) x (a – b)

Question 4.

(x – 1) (x + 1) is equal to ___

Question 5.

The value(RBSESolutions.com)of 3.5 x 3.5 – 2.5 x 2.5 is ___

Answers

1. Identity

2. (a + b)

3. (a + b)

4. x² – 1

5. 6

**III. True/False Type Questions**

Question 1.

Factors of a² – a + ab – a are (a – 1) (a + b).

Question 2.

Expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 2 }\) is \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } +2\)

Question 3.

Factors of x² – 7x + 12 are (x + 3) (x + 4).

Question 4.

If x = 2 and y = – 1 then value of x² + 4xy + 4y² is 0.

Answers

1. True

2. True

3. False

4. True.

**IV. Matching Type Questions**

Part 1 |
Part 2 |

1. 103 × 107 | (a) 11021 |

2. 22y – 33z | (b) 2y |

3. common factor of 2y, 22xy | (c) – 4y |

4. – 36y³ ÷ 9y² | (d) 11 (2y – 3z) |

Answers

1. ⇔ (a)

2. ⇔ (d)

3. ⇔ (b)

4. ⇔ (c)

**V. Very Short Answer Type Questions**

Question 1.

Factorize 3x³ + 3x² + x + 1.

Solution

3x³ + 3x² + x + 1

= 3x² (x + 1) + 1 (x + 1)

= (x + 1) (3x² + 1)

Question 2.

Find common factor of 2(x + y) + 3(x + y) + 5(x + y)

Solution

Common factor is (x + y)

Question 3.

Simplify 2x(2x² + 2x – 9).

Solution

2x (2x² + 2x – 9)

= 2x × 2x² + 2x × 2x – 2x × 9

= 4x³ + 4x² – 18x

Question 4.

Simplify (x + 2) (x + 3).

Solution

(x + 2) (x + 3)

= x² + (2 + 3)x + 2 × 3

= x² + 5x + 6

Question 5.

Find the factor of 4x² – a².

Solution

4x² – a²

= (2x)² – a²

= (2x + a) (2x – a)

Question 6.

If x + y = 20, xy = 34 then find the value of x² + y².

Solution

(x + y)² = x² + y² + 2xy

⇒ (20)² = x² + y² + 2(34)

⇒ 400 = x² + y² + 68

⇒ x² + y² = 400 – 68

⇒ x² + y² = 332

Question 7.

If \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } =62\) then find the value of \(\left( x+\frac { 1 }{ x } \right) \)

Question 8.

If x² – x – 42 = (x + k) (x + 6) then find the value of k.

Solution

x² – x – 42 = (x + k) (x + 6)

⇒ x² – 7x + 6x – 42 = (x + k) (x + 6)

⇒x (x – 7) + 6 (x – 7) = (x + k) (x + 6)

⇒ (x – 7) (x + 6) = (x + k) (x + 6)

On comparison

k = – 7

**VI. Short Answer Type Questions**

Question 1.

Factorize the following expression

x² + 8x + 16

Solution

x² + 8x + 16

= x² + 2 × x + 4 + (4)²

= (x + 4)²

Question 2.

Simplify :

39y^{3} (50y² – 98) ÷ 26y² (5y + 7)

Solution

39y^{3} (50y² – 98) ÷ 26y² (5y + 7)

= 3y (5y – 7)

Question 3.

Divide 8(x^{3}y^{2}z^{2} + x^{2}y^{3}z^{2} + x^{2}y^{2}z^{3}) ÷ 4x^{2}y^{2}z^{2}.

Solution

8(x^{3}y^{2}z^{2} + x^{2}y^{3}z^{2} + x^{2}y^{2}z^{3}) ÷ 4x^{2}y^{2}z^{2}.

= 2x + 2y + 2z

= 2(x + y + z)

Question 4.

Factorize x^{4} – (x – z)^{4}.

Solution

x^{4} – (x – z)^{4}

= (x^{2})^{2} – {(x – z)^{2}}^{2}

= {x^{2} – (x – z)^{2}} {x^{2} + (x – z)^{2}}

= {x – (x – z)} {x + (x – z)} {x^{2} + x^{2} – 2xz + z^{2}}

= z (2x – z) (2x^{2} – 2xz + z^{2})

Question 5.

Factorize 8x^{2}y^{3} (a + b)^{2} + 24x^{3}y^{2} (a + b)^{2} – 16x^{3}y^{3} (a + b)^{2}.

Solution

8x^{2}y^{3} (a + b)^{2} + 24x^{3}y^{2} (a + b)^{2 }– 16x^{3}y^{3} (a + b)^{2}

= 8x^{2}y^{2} (a + b)^{2} [y + 3x – 2xy]

Question 6.

Factorize

(2x + 3y)² – 5(2x + 3y) – 14

Solution

Let 2x + 3y = a

then (2x + 3y)² – 5(2x + 3y) – 14

= a² – 5a – 14

= a² – 7a + 2a – 14

= a(a – 7) + 2(a – 7)

= (a – 7) (a + 2)

= (2x + 3y – 7) (2x + 3y + 2)

Question 7.

Factorize by(RBSESolutions.com)common factor method

p²qr + pq²r + pqr²

(ii) Divide the polynomial

18m^{3} + 6m² + 12m by 3m

Solution

(i) p²qr + pq²r + pqr²

= pqr (p + q + r))

(ii) 18m^{3} + 6m² + 12 m

= 6m (3m² + m + 2)

Now (18m^{3} + 6m^{2} + 12m) ÷ 3m

= 2(3m^{2} + m + 2)

Question 8.

Factorize the expression and divide

(z² – 4z – 12) ÷ (z + 2)

Solution

z² – 4z – 12

= z² – 6z + 2z – 12

= z(z – 6) + 2(z – 6)

= (z – 6) (z + 2)

∴(z² – 4z – 12) + (z + 2)

Question 9.

Factorize the(RBSESolutions.com)following expressions : [Solve any two]

(i) 5pq + 5p + 3q² + 3q

(ii) a² – 5a + 6

(iii) p^{4} – 81

Solution

(i) 5pq + 5p + 3q² + 3q

= (5pq + 3q²) + (5p + 3q)

= q(5p + 3q) + 1(5p + 3 q)

= (5p + 3q)(q + 1)

(ii) a² – 5a + 6

= a² – 3a – 2a + 6

= a(a – 3) – 2(a – 3)

= (a – 3) (a – 2).

(iii) p^{4} – 81

= (p²)² – (9)²

Identity a² – b² = (a + b) (a – b)

= (p² + 9) (p² – 9)

= (p² + 9) [(p)² – (3)²]

= (p² + 9) (p + 3) (p – 3).

We hope the given RBSE Solutions for Class 8 Maths Chapter 10 Factorization Additional Questions will help you. If you have any query regarding Rajasthan Board RBSE Class 8 Maths Chapter 10 Factorization Additional Questions, drop a comment below and we will get back to you at the earliest.

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