The linear factors of 27x³ - 12x are; 3x, (3x - 2) and (3x + 2).
To determine the linear factors of 27x³ - 12x.
By observation, we know that 3x is a common factor of 27x³ and 12x.
In essence, factorisation on this basis yields;
3x (9x² - 4)
However, the question requires that all factors be linear.
Therefore, there's a need to find the linear factors of (9x² - 4).
- Since 9x² is a perfect square (the square of 3x) and 4 is a perfect square too (square of 2).
The difference of two squares mathematical approach can be used to generate the linear factors of (9x² - 4).
- Therefore: (9x² - 4) = (3x - 2) (3x + 2).
Ultimately, the linear factors of 27x³ - 12x are; 3x, (3x - 2) and (3x + 2).
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