Higher June 2018 Paper 5 Q17
17
\[(x + a)(x + 3)(2x + 1) = bx^3 + cx^2 + dx - 12\]Find the value of \(a\), \(b\), \(c\) and \(d\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(a = -4\) \(b = 2\) \(c = -1\) \(d = -25\) | 4 | B4 for 4 correct values | Mark answers first |
| For 3 marks or less, FT 7 + 2 × their a for c and FT 3 + 7 × their a for \(d\) OR B3 for any 3 correct or FT | |||
| OR B2 for any 2 correct or FT or for reaching \(2x^3 + (7 + 2a)x^2 + (3 + 7a)x + 3a\) oe | B2 for a fully correct 3-bracket expansion, could be unsimplified e.g. \(2x^3 + 7x^2 + 2ax^2 + 3x + 7ax + 3a\) | ||
| OR B1 for any one correct or FT or any correct product of two brackets | For B1, \(2x^2 + x + 6x + 3\) or better or \(x^2 + ax + 3x + 3a\) or better or \(2x^2 + 2ax + x + a\) or better For B1 accept terms on a grid | ||