Find the Common Factor in 4x² + 3x: Term-by-Term Analysis

We factored the expression

$4x^2+3x$ into its basic terms:

$4\cdot x\cdot x+3\cdot x$

What common factor can be found in these terms?

First, consider the expression $4x^2+3x$. We want to factor out the greatest common factor of the terms.

Both terms, $4x^2$ and $3x$, contain the factor $x$. Therefore, $x$ is a common factor.

Write each term showing the factor $x$: $4\cdot x\cdot \orange x$ and $3\cdot \orange x$.

The greatest common factor is $x$.