Find the Common Factor in 2x²+7x: Breaking Down Terms

The expression $2x^2+7x$ is broken down into basic terms:

$2\cdot x\cdot x+7\cdot x$

What common factor can be found in these terms?

To solve this problem, we need to find the common factor in the expression $2x^2 + 7x$, which is given as broken down into basic forms: $2 \cdot x \cdot x + 7 \cdot x$.

Let's go through the solution step-by-step:

• Step 1: Examine each term in the expression.
  The first term is $2 \cdot x \cdot x$, equivalent to $2x^2$.
  The second term is $7 \cdot x$.
• Step 2: Identify factors in each term.
  For $2x^2$, we have the factors $2$, $x$, and another $x$.
  For $7x$, the factors are $7$ and $x$.
• Step 3: Determine the common factor across all terms.
  The common factor present in both terms is $x$.

After identifying the shared factor $x$, it can be factored out of both terms in the expression
Factorization: $2x^2 + 7x = x(2x + 7)$.

Therefore, the common factor between the terms is $x$.