This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You've done a great job with these factorisation problems! Let's go through them. a) Factorise 8x^2 + 6x + 1 Your work: Sum (S) = 6 Product (P) = 8 × 1 = 8 The two numbers that multiply to 8 and add to 6 are 4 and 2. 8x^2 + 4x + 2x + 1 (8x^2 + 4x) + (2x + 1) 4x(2x + 1) + 1(2x + 1) (2x + 1)(4x + 1) ✅ Correct. The factorised expression is (2x + 1)(4x + 1). b) Factorise 3x^2 - 8x + 5 Your work: Sum (S) = -8 Product (P) = 3 × 5 = 15 The two numbers that multiply to 15 and add to -8 are -3 and -5. 3x^2 - 3x - 5x + 5 (3x^2 - 3x) + (-5x + 5) 3x(x - 1) - 5(x - 1) (x - 1)(3x - 5) ✅ Correct. Your final answer is correct. Just a minor note on the grouping step you wrote: (3x^2 - 3x) - (5x + 5) would expand to 3x^2 - 3x - 5x - 5, which is not the original expression. It should be (3x^2 - 3x) + (-5x + 5) or 3x^2 - 3x - 5x + 5 directly. However, you correctly factored 3x(x-1) - 5(x-1), so the final result is correct. The factorised expression is (x - 1)(3x - 5). c) Factorise 6x^2 + 11x - 10 Your work: Sum (S) = 11 Product (P) = 6 × (-10) = -60 The two numbers that multiply to -60 and add to 11 are 15 and -4. 6x^2 + 15x - 4x - 10 (6x^2 - 4x) + (15x - 10) 2x(3x - 2) + 5(3x - 2) (3x - 2)(2x + 5) ✅ Correct. The factorised expression is (3x - 2)(2x + 5). d) Factorise 3x^2 + 7x - 6 Your work: Sum (S) = 7 Product (P) = 3 × (-6) = -18 The two numbers that multiply to -18 and add to 7 are 9 and -2. 3x^2 + 9x - 2x - 6 (3x^2 - 2x) + (9x - 6) x(3x - 2) + 3(3x - 2) (x + 3)(3x - 2) ✅ Correct. The factorised expression is (x + 3)(3x - 2). e) Factorise 2x^2 + 5x + 3 Your work: Sum (S) = 5 Product (P) = 2 × 3 = 6 The two numbers that multiply to 6 and add to 5 are 2 and 3. 2x^2 + 2x + 3x + 3 (2x^2 + 2x) + (3x + 3) 2x(x + 1) + 3(x + 1) (2x + 3)(x + 1) ✅ Correct. The factorised expression is (2x + 3)(x + 1). 3 done, 2 left today. You're making progress.