Higher June 2022 Paper 2 Q23
23 Factorise \(\quad 3x^2 - 16x - 12\) [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((3x + 2)(x - 6)\) | B2 | B1 \((3x + a)(x + b)\) where \(ab = -12\) or \(a + 3b = -16\) \(a\) and \(b\) must be integers SC1 \((-3x - 2)(6 - x)\) |
Additional guidance
| Brackets in either order for B2 and B1 and SC1 | |
| \((3x + 6)(x - 2)\) | B1 |
| \((3x + 4)(x - 3)\) or \((3x + 3)(x - 4)\) or \((3x - 3)(x + 4)\) or \((x + 3)(3x - 4)\) | B1 |
| \((3x + 12)(x - 1)\) or \((x - 12)(3x + 1)\) | B1 |
| Some B1 responses may be implied | |
| eg \(3(x + 4)(x - 1)\) implies \((3x + 12)(x - 1)\) | B1 |
| Do not allow answers involving fractions eg \(3(x - 6)\left(x + \dfrac{2}{3}\right)\) | B0 |
| Some examples of B1 with \(a + 3b = -16\) \((3x + 5)(x - 7) \qquad (3x + 8)(x - 8) \qquad (3x - 1)(x - 5) \qquad (3x - 7)(x - 3)\) | |
| \((2 + 3x)\) is equivalent to \((3x + 2)\) etc | |
| Condone use of multiplication signs in B2 or B1 responses | |
| eg \((3x + 2) \times (x - 6)\) | B2 |
| Condone missing closing bracket in B2 or B1 responses | |
| eg \((3x + 6)(x - 2\) | B1 |
| Ignore any attempt to ‘solve’ after B2 or B1 seen |