Higher November 2020 Paper 1R Q14
14 Expand and simplify \(\;(4x + 1)(x - 3)(5x + 6)\)
(3)
| Scheme | Marks |
|---|---|
| \((4x + 1)(x - 3) = 4x^2 - 12x + x - 3\;(= 4x^2 - 11x - 3)\) \((4x + 1)(5x + 6) = 20x^2 + 24x + 5x + 6\;(= 20x^2 + 29x + 6)\) \((x - 3)(5x + 6) = 5x^2 + 6x - 15x - 18\;(= 5x^2 - 9x - 18)\) | M1 |
| \((5x + 6)(4x^2 - 11x - 3) = 20x^3 - 55x^2 - 15x + 24x^2 - 66x - 18\) \((x - 3)(20x^2 + 29x + 6) = 20x^3 + 29x^2 + 6x - 60x^2 - 87x - 18\) \((4x + 1)(5x^2 - 9x - 18) = 20x^3 - 36x^2 - 72x + 5x^2 - 9x - 18\) | M1 |
| \(20x^3 - 31x^2 - 81x - 18\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: for multiplying 2 brackets with at least 3 out of 4 terms correct
M1: (dep) for multiplying the product of the first 2 brackets (ft from the 1st stage) by the 3rd bracket, and getting at least 3 out of 6 or 4 out of 8 terms correct
Alternative
| Scheme | Marks |
|---|---|
| \(20x^3 + 24x^2 - 60x^2 + 5x^2 - 15x + 6x - 72x - 18\) | B2 |
| \(20x^3 - 31x^2 - 81x - 18\) | A1 |
Notes
B2: for at least 6 out of 8 terms correct
(B1 for 4 or 5 out of 8 correct terms)