June 2019 Paper 1 Q10
10 Factorise fully \(\quad 6x^2 + 26xy - 20y^2\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \((6x + ay)(x + by)\) | M1 | \(ab = -20\) or \(a + 6b = 26\) |
| \((6x - 4y)(x + 5y)\) | A1 | |
| \(2(3x - 2y)(x + 5y)\) | A1 | oe but must have 3 correct factors |
| Alternative method 2 | ||
| \((3x + ay)(2x + by)\) | M1 | \(ab = -20\) or \(2a + 3b = 26\) |
| \((3x - 2y)(2x + 10y)\) | A1 | |
| \(2(3x - 2y)(x + 5y)\) | A1 | oe but must have 3 correct factors |
| Alternative method 3 | ||
| \(2(3x^2 + 13xy - 10y^2)\) | M1 | |
| \(2(3x - 2y)(x + 5y)\) | A2 | oe but must have 3 correct factors A1 for correct answer with signs wrong way round ie \(\ 2(3x + 2y)(x - 5y)\) |
| Alternative method 4 using \((3x^2 + 13xy - 10y^2)\) | ||
| \((3x + ay)(x + by)\) | M1 | \(ab = -10\) or \(a + 3b = 13\) |
| \((3x - 2y)(x + 5y)\) | A1 | |
| \(2(3x - 2y)(x + 5y)\) | A1 | oe but must have 3 correct factors |
Additional guidance
| Candidates who remove \(x\) or \(y\), factorise correctly and then replace the letter to gain correct answer | M1A2 |
| Candidates who remove \(x\) or \(y\), factorise correctly and then don’t replace the letter | M0A0 |
| Condone further working in an attempt to solve an equation |