Final answer:
The trinomial '4t⁵-20t⁴+24t³' can be factored completely by finding the GCF first. After factoring the GCF, the trinomial can be factored as '4t³(t - 2)(t - 3)'.
Step-by-step explanation:
The trinomial 4t⁵-20t⁴+24t³ can be factored by finding the Greatest Common Factor (GCF) first. In this case, the GCF is the highest power of 't' that is common to all terms and the highest integer that divides 4, 20, and 24. That would be 4t³.
Factor out the GCF from the original trinomial to get: 4t³(t² - 5t + 6). Now, consider the trinomial inside the parenthesis for further factoring. This standard form quadratic trinomial can be factored as (t - 2)(t - 3). Thus, the original trinomial can be factored completely as 4t³(t - 2)(t - 3).
Learn more about Factoring Trinomials