Factorising: Trinomials, Grouping in Pairs & the Cubes (Grade 10)

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Grade 10 · Algebraic Expressions

MEMORANDUM

Name:

Class:

Date:

Mark

/ 25

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Factorise: 3x² − 12
(2)
3(x² − 4) = 3(x − 2)(x + 2)✓✓ (2)
2
Factorise: x³ + 3x² + 2x + 6
(3)
x²(x + 3) + 2(x + 3) = (x + 3)(x² + 2)✓✓✓ (3)
3
Factorise: ax + ay + bx + by
(2)
a(x + y) + b(x + y) = (x + y)(a + b)✓✓ (2)
4
Factorise: x³ + 27
(2)
(x + 3)(x² − 3x + 9)✓✓ (2)
5
Factorise: x³ − 64
(2)
(x − 4)(x² + 4x + 16)✓✓ (2)
6
Factorise: 8x³ − 1
(3)
(2x − 1)(4x² + 2x + 1)✓✓✓ (3)
7
Factorise: 27x³ + 8
(3)
(3x + 2)(9x² − 6x + 4)✓✓✓ (3)
8
Factorise: x² − 7x + 12
(2)
(x − 3)(x − 4)✓✓ (2)
9
Factorise: 2x² + 7x + 3
(3)
a × c = 6; 6 and 1; 2x² + 6x + x + 3 = 2x(x + 3) + 1(x + 3) = (2x + 1)(x + 3)✓✓✓ (3)
10
Factorise: 2x² − 5x − 3
(3)
a × c = −6; −6 and +1; 2x² − 6x + x − 3 = 2x(x − 3) + 1(x − 3) = (2x + 1)(x − 3)✓✓✓ (3)

TOTAL: 25 marks