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12x²y − 8xy² factorises to 4xy(3x − 2y) and x² − 25 factors as (x − 5)(x + 5), so this Grade 8 sheet opens by pulling out common factors and spotting differences of squares. The key adds (x + 3)(x + 4) for a quadratic.
Key Takeaways
12x²y − 8xy² = 4xy(3x − 2y) (Q1).
x² − 25 = (x − 5)(x + 5) (Q2).
Q3 records (x + 3)(x + 4) as a factorised quadratic.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
The factorised form of 12x²y − 8xy² is:
(a) 4xy(3x − 2y) (b) 4xy(3x + 2y) (c) 4x²y²(3 − 2) (d) 4xy(3y − 2x)
2.
(x² − 25) factorises to:
(a) (x − 5)² (b) (x + 5)² (c) (x − 5)(x + 5) (d) (x − 25)(x + 1)
3.
The factors of x² + 7x + 12 are:
(a) (x + 3)(x + 4) (b) (x − 3)(x + 4) (c) (x + 3)(x − 4) (d) (x − 3)(x − 4)
4.
Which of the following is a factor of 6x² − 5x − 6?
(a) (2x − 3) (b) (3x − 2) (c) (2x + 3) (d) (3x + 2)
5.
What is the common factor in 3a²b + 6ab² + 9ab?
(a) 3 (b) 3ab (c) ab (d) 3a²b²
6.
x² + 6x + 9 = ?
(a) (x + 3)(x − 3) (b) (x + 3)² (c) (x − 3)² (d) (x + 6)(x + 1)
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
Factorise: 6x² + 9x.
8.
Factorise: 25x² − 16y².
9.
Factorise: x² + 9x + 20.
10.
Divide: 15x²y³z ÷ 5xyz.
11.
Factorise: 4x² − 12x + 9.
12.
Factorise: a⁴ − b⁴.
13.
Divide 6x² + 11x + 3 by (2x + 3).
14.
Simplify: (x² − 9) ÷ (x − 3).
Section C: Word Problems (3 Marks Each)
Apply the concepts to solve real-life problems.
15.
The area of a rectangle is (6x² + 19x + 15) sq units and its length is (2x + 3) units. Find its breadth.
16.
A polynomial representing the product of two consecutive integers is n² + n. Factorise it.
17.
Find the side of a square whose area is (4x² + 20x + 25) sq units.
18.
The volume of a cuboid is (x³ − 8) cubic units. If its length and width are (x − 2) and (x² + 2x + 4), find its height.
19.
The cost of (x + 3) books is ₹(x² + 7x + 12). Find the cost of one book in terms of x.
20.
Simplify: (a² − 16)(a² − 4) / (a + 2)(a + 4).
Answer Key
1. a) 4xy(3x − 2y)
2. c) (x − 5)(x + 5)
3. a) (x + 3)(x + 4)
4. a) (2x − 3)
5. b) 3ab
6. b) (x + 3)²
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
How is 12x²y − 8xy² factorised?
4xy(3x − 2y), option (a) in this worksheet (Q1).
How is x² − 25 factorised?
(x − 5)(x + 5), option (c) in this worksheet (Q2).
What is x² + 7x + 12 equal to?
(x + 3)(x + 4), option (a) in this worksheet (Q3).