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 answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

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step-by-step explanation: