Consider the polynomial `P(x) = 2x^3-7x^2-7x+12`.
- Show that `(x-1)` is a factor of `P(x)`. (1 mark)
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- Fully factorise `P(x)`. (2 marks)
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Show Worked Solution
i. `P(1) = 2-7-7+12=0`
`:. (x-1)\ \ text(is a factor of)\ P(x)`
ii. `text{Using part (i)} \ => (x-1)\ text{is a factor of}\ P(x)`
`P(x) = (x-1)*Q(x)`
`text(By long division:)`
| `P(x)` | `= (x-1) (2x^2-5x-12)` |
| `= (x-1)(2x+3)(x-4)` |