Factors of Quadratic Expressions — O/L Mathematics

How do I practise Factors of Quadratic Expressions?

3 questions with worked solutions

1. Factorise completely: 6x² + 11x + 4
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   Step 1: Identify a, b, c: a = 6, b = 11, c = 4. Step 2: Compute ac = 6 × 4 = 24. Step 3: Find two numbers that multiply to 24 and add to 11. The factor pairs of 24 are (1,24), (2,12), (3,8), (4,6). The pair (3,8) gives 3 + 8 = 11. Step 4: Split the middle term: 6x² + 3x + 8x + 4. Step 5: Group and factor: (6x² + 3x) + (8x + 4) = 3x(2x + 1) + 4(2x + 1) = (3x + 4)(2x + 1). Step 6: Verify by expanding: (3x + 4)(2x + 1) = 6x² + 3x + 8x + 4 = 6x² + 11x + 4. Correct.
   Modelled on: the O/L Mathematics examination pattern
2. Factorise: (x + 5)² − 9
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   Recognise as difference of two squares: a² − b² = (a + b)(a − b), with a = (x + 5) and b = 3. So (x + 5)² − 9 = [(x + 5) + 3][(x + 5) − 3] = (x + 8)(x + 2). Verify by expanding: (x + 8)(x + 2) = x² + 2x + 8x + 16 = x² + 10x + 16. Also (x + 5)² − 9 = x² + 10x + 25 − 9 = x² + 10x + 16. Correct.
   Modelled on: the O/L Mathematics examination pattern
3. A rectangular garden has area 3x² + 10x + 8 square metres. Express the length and width as factors of this expression.
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   Factorise 3x² + 10x + 8. a = 3, b = 10, c = 8, ac = 24. Find two numbers multiplying to 24 and adding to 10: 4 and 6. Split: 3x² + 4x + 6x + 8. Group: x(3x + 4) + 2(3x + 4) = (x + 2)(3x + 4). So the sides are (x + 2) m and (3x + 4) m. Check: (x + 2)(3x + 4) = 3x² + 4x + 6x + 8 = 3x² + 10x + 8. Correct.
   Modelled on: the O/L Mathematics examination pattern

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Where does Factors of Quadratic Expressions fit in the syllabus?

Grade 10 · Term 1