Find the Common Factor in 2x²+7x: Step-by-Step Factorization

To solve this problem, we'll focus on finding the greatest common factor of the expression $2x^2 + 7x$.

• Step 1: Identify the given expression $2x^2 + 7x$.
• Step 2: Look for common factors:
  • In the term $2x^2$, the factors are $2$, $x$, and $x$.
  • In the term $7x$, the factors are $7$ and $x$.
• Step 3: Notice that the common factor here is $x$, as it is present in both terms.
• Step 4: Factor $x$ out of each term in the expression:
  $2x^2 + 7x = x(2x) + x(7) = x(2x + 7)$

Therefore, the expression $2x^2 + 7x$ can be factorized as $x(2x + 7)$.

This corresponds to choice 3, which is $x(2 \cdot x + 7)$.

The factorized expression is $x(2x + 7)$.