Question

factor completely.
$3s^{2}+8 + 8s+3s^{3}$

Explanation:

Step1: Rearrange the terms

First, we rearrange the given polynomial \(3s^{2}+8 + 8s+3s^{3}\) in descending order of the powers of \(s\). So we get \(3s^{3}+3s^{2}+8s + 8\).

Step2: Group the terms

We group the first two terms and the last two terms together: \((3s^{3}+3s^{2})+(8s + 8)\).

Step3: Factor out the GCF from each group

For the first group \(3s^{3}+3s^{2}\), the greatest common factor (GCF) is \(3s^{2}\). Factoring out \(3s^{2}\), we have \(3s^{2}(s + 1)\).
For the second group \(8s+8\), the GCF is \(8\). Factoring out \(8\), we get \(8(s + 1)\).
So now the polynomial becomes \(3s^{2}(s + 1)+8(s + 1)\).

Step4: Factor out the common binomial factor

We can see that both terms have a common binomial factor of \((s + 1)\). Factoring out \((s + 1)\), we get \((s + 1)(3s^{2}+8)\).

Answer:

\((s + 1)(3s^{2}+8)\)