Higher November 2021 Paper 3 Q25
25 Expand and simplify fully \(\qquad (x - 3)(x + 2)(x + 5)\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – multiplies \((x - 3)(x + 2)\) first | ||
| \(x^2 - 3x + 2x - 6\) or \(x^2 - x - 6\) | M1 | four terms with at least three correct implied by \(x^2 - x \pm k\) where \(k\) is a non-zero constant |
| \(x^3 - 3x^2 + 2x^2 - 6x + 5x^2 - 15x + 10x - 30\) or \(x^3 - x^2 - 6x + 5x^2 - 5x - 30\) | M1dep | full expansion with correct multiplication of their 3 or 4 terms by \(x\) and 5 |
| \(x^3 + 4x^2 - 11x - 30\) | A1 | |
| Alternative method 2 – multiplies \((x - 3)(x + 5)\) first | ||
| \(x^2 - 3x + 5x - 15\) or \(x^2 + 2x - 15\) | M1 | four terms with at least three correct implied by \(x^2 + 2x \pm k\) where \(k\) is a non-zero constant |
| \(x^3 - 3x^2 + 5x^2 - 15x + 2x^2 - 6x + 10x - 30\) or \(x^3 + 2x^2 - 15x + 2x^2 + 4x - 30\) | M1dep | full expansion with correct multiplication of their 3 or 4 terms by \(x\) and 2 |
| \(x^3 + 4x^2 - 11x - 30\) | A1 | |
| Alternative method 3 – multiplies \((x + 2)(x + 5)\) first | ||
| \(x^2 + 2x + 5x + 10\) or \(x^2 + 7x + 10\) | M1 | four terms with at least three correct implied by \(x^2 + 7x \pm k\) where \(k\) is a non-zero constant |
| \(x^3 + 2x^2 + 5x^2 + 10x - 3x^2 - 6x - 15x - 30\) or \(x^3 + 7x^2 + 10x - 3x^2 - 21x - 30\) | M1dep | full expansion with correct multiplication of their 3 or 4 terms by \(x\) and \(-3\) |
| \(x^3 + 4x^2 - 11x - 30\) | A1 | |
Additional guidance
Do not ignore further incorrect simplification or attempt to solve after correct answer seen