Question

factor $16v^{5} + 16v^{3}$ completely.

Explanation:

Step1: Identify greatest common factor

The GCF of $16v^5$ and $16v^3$ is $16v^3$. Factor it out:
$16v^5 + 16v^3 = 16v^3(v^2 + 1)$

Step2: Check for further factoring

The quadratic $v^2 + 1$ cannot be factored over real numbers, as it has no real roots.

Answer:

$16v^3(v^2 + 1)$