Factorize the Expression: Finding Common Factor in 5x+2x

To solve this problem, we'll follow these steps:

• Step 1: Determine the common factor in both terms of the expression $5x + 2x$.
• Step 2: Factor out the common factor using the distributive property.
• Step 3: Verify the answer against the multiple choices provided.

Now, let's work through each step:
Step 1: In the expression $5x + 2x$, the common factor between the two terms is $x$.

Step 2: By applying the distributive property in reverse, we take $x$ out of each term, which gives us:

$x(5) + x(2) = x(5 + 2)$

Therefore, the expression can be factorized as:

$x(5 + 2)$

Step 3: Upon examining the options provided:

• Choice 1: $5(x + 2x)$
• Choice 2: $2 \cdot x(3 \cdot x)$
• Choice 3: $2 \cdot x(3 \cdot x + 1)$
• Choice 4: $x(5 + 2)$

The correct factorization corresponds to Choice 4: $x(5 + 2)$.

Hence, the factorized expression is $x(5 + 2)$, which is the correct choice.