Final answer:
To factor the expression completely, we need to factor each term separately. Once we factor each term, we can put them together to get the completely factored expression.
Step-by-step explanation:
To factor the expression completely, we can start by factoring each term separately.
First, let's factor 3x³. The largest exponent of x is 3, so we know that x is a factor. Dividing 3x³ by x gives us 3x².
Next, let's factor (3x-4)². This is a perfect square trinomial, so we can write it as (3x-4)(3x-4), which gives us 9x²-24x+16.
Lastly, let's factor x⁴(8)(3x-4)(3). The terms x⁴ and 8 have no common factors, so we can leave them as they are. The terms (3x-4) and (3) are already factored.
Putting it all together, the completely factored expression is 3x²(9x²-24x+16)(8)(3x-4)(3).