The correct linear factors of the polynomial

To factor the polynomial \(20x^3 - 96x^2 - 144x\), you can start by factoring out the greatest common factor (GCF) from all the terms.

The GCF of the coefficients \(20\), \(-96\), and \(-144\) is \(4\), and all terms have at least one factor of \(x\). Thus, we can factor out \(4x\):

\[
20x^3 - 96x^2 - 144x = 4x(5x^2 - 24x - 36)
\]

Next, we need to factor the quadratic \(5x^2 - 24x - 36\). We can look for two numbers that multiply to \(5 \times -36 = -180\) and add to \(-24\). The numbers that meet these criteria are \(-30\) and \(6\).

Now we can split the middle term and factor by grouping:

\[
5x^2 - 30x + 6x - 36
\]

Grouping gives us:

\[
(5x^2 - 30x) + (6x - 36)
\]

Factoring each group results in:

\[
5x(x - 6) + 6(x - 6)
\]

Now we can factor out the common binomial factor \(x - 6\):

\[
(5x + 6)(x - 6)
\]

Putting it all together, we have:

\[
20x^3 - 96x^2 - 144x = 4x(5x + 6)(x - 6)
\]

Thus, the correct linear factors of the polynomial \(20x^3 - 96x^2 - 144x\) are:

\[
\boxed{4x(5x + 6)(x - 6)}
\]