Factor the expression $3x(x+1) + 7(x+1)$.
We can factor the expression $x+1$ out of each term: \[3x(x+1) + 7(x+1) = \boxed{(3x+7)(x+1)}.\]
(3x+7)(x+1)
Level 3
Algebra
Problem: Factor the expression $3x(x+1) + 7(x+1)$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To factor the expression, first identify common factors in the terms. The expression consists of two parts: $3x(x+1)$ and $7(x+1)$. Notice that both terms share a common factor of $(x+1)$. 

Next, apply the distributive property in reverse. This involves factoring out the common factor $(x+1)$ from both terms. 

Rewrite the expression as follows: 
1. Factor out $(x+1)$: 
   - From $3x(x+1)$, when $(x+1)$ is factored out, the remaining term is $3x$.
   - From $7(x+1)$, when $(x+1)$ is factored out, the remaining term is $7$.

Now combine the remaining terms:
2. The expression can be rewritten as $(x+1)(3x + 7)$.

Finally, rearranging the terms gives the factored form:
3. The final answer is $(3x + 7)(x + 1)$. 

This shows the complete factoring process, confirming that the expression is correctly factored into the product of two binomials.<|END_OF_LATENT|> The final answer is $(3x+7)(x+1)$.