# How do you factor 3x^2 - 6x?

$3 x \left(x - 2\right)$
The term $3 {x}^{2}$ can be thought of as $3 x \cdot x$ and the term $6 x$ can be thought of as $3 x \cdot 2$. The $3 x$ is therefore a common factor that can be factored out (reversing the distributive property), and keeping the minus sign in place: $3 {x}^{2} - 6 x = 3 x \left(x - 2\right)$.
This also implies that the roots ($x$-intercepts) of the function $f \left(x\right) = 3 {x}^{2} - 6 x = 3 x \left(x - 2\right)$ are $x = 0$ and $x = 2$.