Higher June 2022 Paper 3 Q27
27 Expand and simplify fully \(\quad (x - 3)(x - 4)(x + 8)\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: multiplies \((x - 3)(x - 4)\) first | ||
| \(x^2 - 3x - 4x + 12\) or \(x^2 - 7x + 12\) | M1 | four terms with at least three correct implied by \(x^2 - 7x + k\) where \(k\) is a non-zero constant |
| \(x^3 - 3x^2 - 4x^2 + 12x + 8x^2 - 24x - 32x + 96\) or \(x^3 - 7x^2 + 12x + 8x^2 - 56x + 96\) | M1dep | full expansion with correct multiplication of their 3 or 4 terms by \(x\) and 8 |
| \(x^3 + x^2 - 44x + 96\) | A1 | |
| Alternative method 2: multiplies \((x - 3)(x + 8)\) first | ||
| \(x^2 - 3x + 8x - 24\) or \(x^2 + 5x - 24\) | M1 | four terms with at least three correct implied by \(x^2 + 5x + k\) where \(k\) is a non-zero constant |
| \(x^3 - 3x^2 + 8x^2 - 24x - 4x^2 + 12x - 32x + 96\) or \(x^3 + 5x^2 - 24x - 4x^2 - 20x + 96\) | M1dep | full expansion with correct multiplication of their 3 or 4 terms by \(x\) and \(-4\) |
| \(x^3 + x^2 - 44x + 96\) | A1 | |
| Alternative method 3: multiplies \((x - 4)(x + 8)\) first | ||
| \(x^2 - 4x + 8x - 32\) or \(x^2 + 4x - 32\) | M1 | four terms with at least three correct implied by \(x^2 + 4x + k\) where \(k\) is a non-zero constant |
| \(x^3 - 4x^2 + 8x^2 - 32x - 3x^2 + 12x - 24x + 96\) or \(x^3 + 4x^2 - 32x - 3x^2 - 12x + 96\) | M1dep | full expansion with correct multiplication of their 3 or 4 terms by \(x\) and \(-3\) |
| \(x^3 + x^2 - 44x + 96\) | A1 | |
Additional guidance
Do not award A mark if further incorrect simplification or attempt to solve after correct answer seen
For method marks, terms may be given in a table with correct signs shown