FACTORIZATION AND ALGEBRAIC MANIPULATION

1

What is the HCF of 8x³y and 12x²y²?

A 4x²y B 24x³y² C 4x³y² D 8x²y

2

Farah needs the LCM of 10a²b and 15ab². She takes the highest powers. What is the LCM?

A 30a²b² B 30ab C 150a²b² D 5ab

3

Sana needs to find the LCM of 4x² and 6x³. She lists the multiples of each. What is the LCM?

A 12x⁵ B 12x³ C 24x³ D 2x²

4

Find the HCF of x² + x - 6 and x² + 4x + 3.

A x + 3 B x - 2 C x + 1 D x - 3

5

Beenish is factorizing x² + 8x + 15. She needs two numbers with product 15 and sum 8. What is the factorization?

A (x + 3)(x + 5) B (x + 1)(x + 15) C (x - 3)(x - 5) D (x + 8)(x + 1)

6

Usman is simplifying the algebraic fraction (x² - 4)/(x + 2). He factors the numerator first. What is the simplified form?

A x - 2 B x + 2 C x² - 2 D (x - 2)/(x + 2)

7

Zeeshan is subtracting 9/(x + 4) - 5/(x + 4). The denominators are the same. What is the difference?

A 4/(x + 4) B 14/(x + 4) C 4/(x + 4)² D 45/(x + 4)

8

Factorize: 2x² - 18

A 2(x - 3)(x + 3) B 2(x² - 9) C 2(x - 3)² D (2x - 6)(x + 3)

9

Ayesha is adding the fractions 1/x + 1/y. She finds a common denominator. What is the sum?

A (x + y)/xy B 2/(x + y) C (x + y)/(x + y) D xy/(x + y)

10

Simplify: (x + 2)/(x² - 4) × (x - 2)/(x + 1)

A 1/(x + 1) B (x - 2)/(x + 1) C (x + 2)/(x + 1) D 1/(x - 1)

11

Factorize completely: x² - 6x + 9 - y²

A (x - 3 - y)(x - 3 + y) B (x - 3 - y)² C (x + 3 - y)(x + 3 + y) D (x - 3)(x - 3) - y²

12

Saba is adding 3/(x + 2) + 4/(x + 2). Since denominators are the same, she adds numerators. What is the sum?

A 7/(x + 2) B 12/(x + 2) C 7/(x + 2)² D 7/(2x + 4)

13

Kashif is simplifying (x² - 9)/(x² + 6x + 9). He factors both numerator and denominator. What is the simplified form?

A (x - 3)/(x + 3) B (x + 3)/(x - 3) C (x - 3)/(x + 3)² D 1

14

Nashit is simplifying (x² + 7x + 10)/(x + 5). He factors the numerator. What is the simplified form?

A x + 2 B x + 5 C x - 2 D x² + 2

15

Saima is multiplying (x + 1)/x × x²/(x + 1). She cancels common factors. What is the product?

A x B 1/x C x² D x + 1

16

Simplify: (x² - 1)/(x² + 2x + 1) ÷ (x - 1)/(x + 1)

A 1 B x + 1 C x - 1 D (x + 1)/(x - 1)

17

Factorize: 6x² - 7x - 3

A (3x + 1)(2x - 3) B (3x - 1)(2x + 3) C (6x + 1)(x - 3) D (2x + 1)(3x - 3)

18

Saad is finding the HCF of 8x³y² and 12x²y³. He takes the lowest powers. What is the HCF?

A 4x²y² B 4x³y³ C 24x³y³ D 2x²y²

19

Find the HCF of 12x³y² and 18x²y³.

A 6x²y² B 36x³y³ C 6x³y³ D 12x²y²

20

Simplify: (x² + 4x + 3)/(x² - 1) × (x - 1)/(x + 3)

A 1 B x + 1 C x - 1 D (x + 1)/(x - 1)

21

Factorize: x² + 2x - 15

A (x + 5)(x - 3) B (x - 5)(x + 3) C (x + 5)(x + 3) D (x - 5)(x - 3)

22

Tariq is factorizing 2x² + 8x. He takes out the common factor. What is the factored form?

A 2x(x + 4) B 2(x² + 4x) C x(2x + 8) D 2x(x + 8)

23

Factorize: x² - 4x - 12

A (x - 6)(x + 2) B (x + 6)(x - 2) C (x - 4)(x + 3) D (x + 4)(x - 3)

24

What is the square root of (4x² + 12x + 9)?

A 2x + 3 B 2x - 3 C 4x + 3 D 2x + 9

25

Factorize: x² - 10x + 25 - 4y²

A (x - 5 - 2y)(x - 5 + 2y) B (x + 5 - 2y)(x + 5 + 2y) C (x - 5 - 2y)² D (x - 5)² - 4y²