Factorisation quiz

The highest common factor of 12x^2y and 18xy^2 is:

The factorised form of x^2 - 25 is:

x^2 + 8x + 16 is equal to:

The factors of m^2 + 7m + 12 are:

15x^3 divided by 5x is:

The factorised form of 5x - 15 is:

y^2 - 6y + 9 is equal to:

The irreducible factors of 14pq are:

(p^2 - 9) divided by (p - 3) gives:

Which of the following is correct?

Factorise 12x^2 - 8x and check your answer by multiplication. (2 marks)

Factorise 6xy - 4y + 6 - 9x by regrouping. (2 marks)

Factorise 9x^2 - 16y^2. (2 marks)

Factorise 25m^2 + 30m + 9. (2 marks)

Factorise y^2 + 2y - 15 and verify by multiplication. (2 marks)

Divide 24(x^2yz + xy^2z + xyz^2) by 8xyz. (2 marks)

A student wrote 3x + 4x = 7x^2. Find the error and correct it. Check by substituting x = 2. (2 marks)

Factorise 2x^3 - 8x completely. (2 marks)

Divide (10x - 25) by 5, and then by (2x - 5). (2 marks)

Factorise x^2 - 2xy + y^2 - z^2. (2 marks)

Using factorisation, evaluate: (i) 98^2 - 2^2 (ii) 1.5^2 - 0.5^2 (iii) 87 x 13 + 87 x 87. (3 marks)

Carry out the divisions: (i) (x^3 + 2x^2 + 3x) by 2x (ii) (p^3q^6 - p^6q^3) by p^3q^3 (iii) 96xyz(3x - 12)(5y - 30) by 144(x - 4)(y - 6). (3 marks)

The area of a square plot is (9x^2 + 24x + 16) m^2. Find an expression for its side. Find the side and the perimeter when x = 2. (3 marks)

The volume of a cuboid is (3x^2 - 27) cm^3. Factorise the expression to find possible dimensions of the cuboid, and check that the volume agrees when x = 5. (3 marks)

Using factorisation, evaluate: (i) 999 x 1001 + 1 (ii) 64^2 - 36^2 (iii) 153^2 - 147^2. (3 marks)

Read the passage and answer the questions. The area of a rectangular kitchen garden is given by the expression (x^2 + 9x + 20) m^2, where x is a positive number. (i) Factorise the expression to find the length and breadth of the garden. (ii) Find the area when x = 6. (iii) Find an expression for the perimeter and its value when x = 6. (5 marks)

Read the passage and answer the questions. Kiran did her factorisation homework and wrote: x^2 + 5x + 6 = (x + 2)(x + 3); 4x^2 - 9 = (2x - 3)^2; (6x + 9)/3 = 2x + 9. (i) Verify the first answer by multiplication. (ii) Find the error in the second answer and correct it. (iii) Find the error in the third answer and correct it. (5 marks)

Read the passage and answer the questions. A teacher has (x^2 + 11x + 30) sweets and distributes them equally among (x + 5) students so that none is left over. (i) Find, by factorising, the number of sweets each student gets. (ii) If x = 10, find the total number of sweets, the number of students and the sweets per student. (iii) Explain why the sweets could be shared without any remainder. (5 marks)

Read the passage and answer the questions. Chairs for a school function are arranged in equal rows. The total number of chairs is given by the expression 5xy + 10x + 3y + 6. (i) Factorise the expression by regrouping. (ii) If the number of rows is (y + 2), how many chairs are there in each row? (iii) Find the total number of chairs when x = 4 and y = 10, using both the factorised and the original forms. (5 marks)

Read the passage and answer the questions. A square floor of side x m has a square platform of side 4 m in one corner, so the area left for tiling is (x^2 - 16) m^2. (i) Factorise the area left for tiling. (ii) Find the area left for tiling when x = 10. (iii) Explain how the remaining L-shaped region can be rearranged into a rectangle and give its length and breadth. (5 marks)

Describe the methods of factorisation studied in this chapter, with one example each. Factorise: (i) 4x^2y - 8xy^2 (ii) x^2 + xy + 8x + 8y (iii) 16x^4 - 81 (iv) p^2 - 13p + 40. (6 marks)

Draw algebra tile diagrams for x^2 + 6x + 8 and x^2 + 6x + 9, arranging each set of tiles into a rectangle. Label the sides and write the factorisation of each. Explain why the second arrangement is a square. (6 marks)

Explain how a polynomial is divided by another polynomial by first factorising. Divide: (i) 4yz(z^2 + 6z - 16) by 2y(z + 8) (ii) 5pq(p^2 - q^2) by 2p(p + q) (iii) 12xy(9x^2 - 16y^2) by 4xy(3x + 4y). (6 marks)

Draw a diagram showing a square of side x with a square of side y removed from a corner, and by cutting and rearranging show that x^2 - y^2 = (x + y)(x - y). Use the identity to factorise 49p^2 - 81q^2 and to evaluate 105^2 - 95^2. (6 marks)

Find and correct the errors: (i) 2x + 3y = 5xy (ii) -(x - 4) = -x - 4 (iii) (x + 5)^2 = x^2 + 25 (iv) 7x/7x = 0 (v) (x + 4)/4 = x + 1. Explain how substituting a number for the variable helps to check an answer. (6 marks)