Finding Common Factors in 5x²+10x: Step-by-Step Factoring

We factored the expression

$5x^2+10x$ into its basic terms:

$5\cdot x\cdot x+2\cdot5\cdot x$

What common factor can be found in these terms?

First, consider the expression $5x^2+10x$. We want to factor out the greatest common factor of the terms.

Write each term showing the factor $x$: $\blue 5\cdot \orange x\cdot x$ and $2\cdot\blue5\cdot \orange x$.

Both terms, $5x^2$ and $10x$, contain the factor $x$ as well as $5$. Therefore, $5\cdot x$ is a common factor.

The greatest common factor is $5\cdot x$.