Higher June 2023 Paper 3 Q12
12 Show that \((x - 1)(x + 3)(x - 5)\) can be written in the form \(ax^3 + bx^2 + cx + d\) where \(a\), \(b\), \(c\) and \(d\) are integers. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Shown | M1 | for a method to find the product of two linear expressions (3 out of 4 terms correct or 4 correct terms ignoring signs) eg \(x^2 + 3x - x - 3\) or \(x^2 + 3x - 5x - 15\) or \(x^2 - 5x - x + 5\) |
| M1 | for a complete method to obtain all terms, half of which are correct (ft their first product) eg \(x^3 - 5x^2 - 10x + 2x^2 - 3x + 15\) | |
| A1 | for \(x^3 - 3x^2 - 13x + 15\) shown, accept \(x^3 + {-3x^2} + {-13x} + 15\) |
Additional guidance
Note that (eg) \(2x - 3\) in expansion of \((x - 1)(x + 3)\) is to be regarded as 3 correct terms.
First product must be quadratic with at least 3 terms but need not be simplified or may be simplified incorrectly