Factorising: The Complete Exam Guide (Every Type) — Worksheet & Memo

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Grade 9 · Algebra

Factorising: The Complete Exam Guide (Every Type)

MEMORANDUM

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/ 30

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 5x + 15 (common factor)
(2)
HCF is 5 → 5(x + 3)✓✓ (2)
2
Factorise 8a²b − 12ab (common factor)
(2)
HCF is 4ab → 4ab(2a − 3)✓✓ (2)
3
Factorise x² − 49 (difference of squares)
(2)
x² = x, 49 = 7 → (x + 7)(x − 7)✓✓ (2)
4
Factorise 25x² − 9 (difference of squares)
(2)
25x² = 5x, 9 = 3 → (5x + 3)(5x − 3)✓✓ (2)
5
Factorise 3x² − 27 (common factor first)
(2)
= 3(x² − 9) = 3(x + 3)(x − 3)✓✓ (2)
6
Factorise x² + 9x + 20 (trinomial, both +)
(2)
Product 20, sum 9 → 4 and 5 → (x + 4)(x + 5)✓✓ (2)
7
Factorise x² − 8x + 15 (trinomial, c + b −)
(2)
Product 15, sum −8 → −3 and −5 → (x − 3)(x − 5)✓✓ (2)
8
Factorise x² + 2x − 15 (trinomial, c −)
(2)
Product −15, sum +2 → +5 and −3 → (x + 5)(x − 3)✓✓ (2)
9
Factorise x² − 2x − 15 (trinomial, c −)
(2)
Product −15, sum −2 → −5 and +3 → (x − 5)(x + 3)✓✓ (2)
10
Factorise 2x² + 7x + 6 (leading coefficient)
(2)
ac = 12, numbers 4 and 3 → 2x² + 4x + 3x + 6 = 2x(x + 2) + 3(x + 2) = (x + 2)(2x + 3)✓✓ (2)
11
Factorise 3x² − 10x + 8 (leading coefficient)
(2)
ac = 24, numbers −6 and −4 → 3x² − 6x − 4x + 8 = 3x(x − 2) − 4(x − 2) = (x − 2)(3x − 4)✓✓ (2)
12
Factorise ax + ay + bx + by (grouping)
(2)
a(x + y) + b(x + y) = (x + y)(a + b)✓✓ (2)
13
Factorise x³ + 4x² + 2x + 8 (grouping)
(2)
x²(x + 4) + 2(x + 4) = (x + 4)(x² + 2)✓✓ (2)
14
Factorise 4x² − 100 (mixed)
(2)
= 4(x² − 25) = 4(x + 5)(x − 5)✓✓ (2)
15
Factorise 2x² − 2x − 24 (mixed)
(2)
= 2(x² − x − 12) = 2(x − 4)(x + 3)✓✓ (2)

TOTAL: 30 marks