Final answer:
The expression 32a⁵ + 24a³ factored out by the greatest common factor is 8a³(4a² + 3).
Step-by-step explanation:
To write the expression 32a⁵ + 24a³ in factored form by factoring out the greatest common factor (GCF), we must find the highest number and the highest power of a that divides both terms evenly. The GCF of 32 and 24 is 8, and the lowest power of that appears in both terms is a³. Therefore, we can factor out 8a³.
The expression breaks down into:
32a⁵ = 8a³ × 4a²
24a³ = 8a³ × 3
So, the factored form is 8a³(4a² + 3).