Factor by grouping. 3u^3+7u^2+3u+7 square

To factor the polynomial $3u^3 + 7u^2 + 3u + 7$ by grouping, we can follow these steps:

1. **Group the terms in pairs:**
$$(3u^3 + 7u^2) + (3u + 7)$$

2. **Factor out the greatest common factor (GCF) from each pair:**
- For the first group $(3u^3 + 7u^2)$, the GCF is $u^2$:
$$u^2(3u + 7)$$
- For the second group $(3u + 7)$, there is no common factor other than 1, so we leave it as is:
$$1(3u + 7)$$

3. **Rewrite the expression using the factored groups:**
$$u^2(3u + 7) + 1(3u + 7)$$

4. **Factor out the common binomial factor $(3u + 7)$:**
$$(3u + 7)(u^2 + 1)$$

So, the factored form of the polynomial $3u^3 + 7u^2 + 3u + 7$ is:
$$\boxed{(3u + 7)(u^2 + 1)}$$