Higher June 2019 Paper 2 Q26
26
\[(x + 5)(x + 2)(x + a) \equiv x^3 + bx^2 + cx - 30\]Work out the values of the integers \(a\), \(b\) and \(c\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \((a =)\ {-3}\) | B1 | |
| \((b =)\ 4\) | B1ft | ft \(7 +\) their \(a\) correct or ft |
| \((c =)\ {-11}\) | B1ft | ft \(10 + 7 \times\) their \(a\) correct or ft |
| Alternative method 2 | ||
| \(x^3 + 5x^2 + 2x^2 + 10x + ax^2 + 5ax + 2ax + 10a\) or \(x^3 + 7x^2 + 10x + ax^2 + 7ax + 10a\) or \(10a = -30\) or \(a = -3\) | M1 | oe terms may be seen in a grid implied by \(x^3 + 5x^2 + 2x^2 + 10x - 3x^2 - 15x - 6x - 30\) or \(x^3 + 7x^2 + 10x - 3x^2 - 21x - 30\) |
| \(5 + 2 +\) their \(a = b\) or \(b = 4\) or \(10 +\) their \(5a +\) their \(2a = c\) or \(c = -11\) or \(x^3 + 4x^2 - 11x - 30\) | M1dep | oe eg \(5x^2 + 2x^2 +\) their \(ax^2 = bx^2\) or \(10x +\) their \(5ax +\) their \(2ax = cx\) |
| \(a = -3\) and \(b = 4\) and \(c = -11\) | A1 | |
Additional guidance
| Apply the scheme that awards most marks | |
| Allow \(x10\) for \(10x\) etc | |
| \(a = -3 \quad b = 4 \quad c = -11\) in working with one or both negative signs omitted on answer lines | B2 |
| \(a = -3 \quad b = 4 \quad c = -11\) in working with values in a different order on answer lines | B2 |