# How do you factor the expression 3x - 9x^2?

Feb 28, 2016

$3 x \left(1 - 3 x\right)$

#### Explanation:

Recall that the greatest common factor is the largest number which two numbers can be divided by without producing a decimal . For example, the greatest common factor of $12$ and $16$ is $4$.

In addition, recall the distributive property: $a \left(b + c\right) = a b + a c$.

Factoring the Expression
$1$. Determine the greatest common factor for $\textcolor{red}{3}$ and $\textcolor{b l u e}{9}$, which is $\textcolor{p u r p \le}{3}$. Using the distributive property, factor $\textcolor{p u r p \le}{3}$ from the expression.

$\textcolor{red}{3} x - \textcolor{b l u e}{9} {x}^{2}$

$= \textcolor{p u r p \le}{3} \left(x - 3 {x}^{2}\right)$

$2$. Both terms, $\textcolor{\mathmr{and} a n \ge}{x}$ and $- 3 \textcolor{t u r q u o i s e}{{x}^{2}}$, contain another common factor, $\textcolor{g r e e n}{x}$. Thus, factor out $\textcolor{g r e e n}{x}$ from the expression.

$= 3 \textcolor{g r e e n}{x} \left(1 - 3 x\right)$