Determine the linear factors for 27x^3-12x

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).

The difference of two squares mathematical approach can be used to generate the linear factors of (9x² - 4).

Ultimately, the linear factors of 27x³ - 12x are; 3x, (3x - 2) and (3x + 2).

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27x^3 - 12x factors into

3(9x^3 - 4x) a common factor of three has been taken out.

3x(9x^2 - 4) a common factor of x has been taken out. 3x is not a linear factor.

9x^2 - 4 factors by means of the difference of squares

3x(3x - 2)(3x + 2)

The two linear factors are 3x - 2 and 3x + 2

the solution is h=10 because you add 9 to each side of the equation.