Question 1: Find the factorization that is equivalent to $x(x+4) - 2(x+4)$. Question 2: Find the factorization that is equivalent to $4x(x+1) - 5(x+1)$.

1. Problem Description

Question 1: Find the factorization that is equivalent to $x(x+4) - 2(x+4)$.

Question 2: Find the factorization that is equivalent to $4x(x+1) - 5(x+1)$.

2. Solution Steps

Question 1:

The given expression is $x(x+4) - 2(x+4)$.

We can factor out the common term $(x+4)$ from both terms:

$x(x+4) - 2(x+4) = (x-2)(x+4)$.

Question 2:

The given expression is $4x(x+1) - 5(x+1)$.

We can factor out the common term $(x+1)$ from both terms:

$4x(x+1) - 5(x+1) = (4x-5)(x+1)$.

3. Final Answer

Question 1: $(x-2)(x+4)$

Question 2: $(4x-5)(x+1)$