Find the Common Factor in 3x²+9x: Breaking Down Terms

We factored the expression

$3x^2+9x$ into its basic terms:

$3\cdot x\cdot x+9\cdot x$

What common factor can be found in these terms?

First, consider the expression $3x^2+9x$. We want to factor out the greatest common factor of the terms.

Both terms, $3x^2$ and $9x$, contain the factor$x$. Therefore, $x$ is a common factor.

Write each term showing the factor $x$: $3\cdot x\cdot\orange x$ and $9\cdot\orange x$.

However, we can further more factor the number $9$, to $3\cdot3$.

So, we can see there's another common factor,$3$, as we can see in both terms: $\blue3\cdot x\cdot x$ and $\blue3\cdot3\cdot x$.

$\blue3\cdot x\cdot\orange x$ and $\blue 3\cdot3\cdot \orange x$

The greatest common factor is then $3x$.