Factorising Algebraic Expressions (Grade 9) — Worksheet & Memo

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Grade 9 · Algebraic Expressions

Factorising Algebraic Expressions (Grade 9)

MEMORANDUM

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Mark

/ 31

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)
(1)
HCF is 5 → 5(x + 3)✓ (1)
2
Factorise 8a²b − 12ab (common factor)
(2)
HCF is 4ab → 4ab(2a − 3)✓✓ (2)
3
Factorise x² − 49 (difference of squares)
(1)
√x² = x, √49 = 7 → (x + 7)(x − 7)✓ (1)
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 + 14x + 20 (common factor, then trinomial)
(3)
= 2(x² + 7x + 10); product 10, sum 7 → 2 and 5 → 2(x + 2)(x + 5)✓✓✓ (3)
11
Factorise 5x² − 5x − 30 (common factor, then trinomial)
(3)
= 5(x² − x − 6); product −6, sum −1 → −3 and +2 → 5(x − 3)(x + 2)✓✓✓ (3)
12
Factorise x²y − 9y (common factor, then difference of squares)
(2)
= y(x² − 9) = y(x + 3)(x − 3)✓✓ (2)
13
Factorise a² − 6a + 9 (trinomial)
(2)
Product 9, sum −6 → −3 and −3 → (a − 3)(a − 3) = (a − 3)²✓✓ (2)
14
Factorise 4x² − 100 (mixed)
(2)
= 4(x² − 25) = 4(x + 5)(x − 5)✓✓ (2)
15
Factorise 2x² − 2x − 24 (mixed)
(3)
= 2(x² − x − 12) = 2(x − 4)(x + 3)✓✓✓ (3)

TOTAL: 31 marks