Question

factor completely. \\(3s^{3} + 6s^{2} + 8s + 16\\)

Explanation:

Step1: Group the terms

We can group the first two terms and the last two terms together:
$$(3s^{3}+6s^{2})+(8s + 16)$$

Step2: Factor out the GCF from each group

For the first group \(3s^{3}+6s^{2}\), the greatest common factor (GCF) is \(3s^{2}\), so we factor that out:
\(3s^{2}(s + 2)\)
For the second group \(8s+16\), the GCF is \(8\), so we factor that out:
\(8(s + 2)\)
Now our expression becomes:
\(3s^{2}(s + 2)+8(s + 2)\)

Step3: Factor out the common binomial factor

We can see that both terms have a common factor of \((s + 2)\), so we factor that out:
\((s + 2)(3s^{2}+8)\)

Answer:

\((s + 2)(3s^{2}+8)\)