# How do you factor completely 9xy^2 - 24xy + 15x?

Nov 26, 2015

$3 x \left(3 y - 5\right) \left(y - 1\right)$

#### Explanation:

$x$ is a factor of everything so we can take that out. Also 3 is likewise a factor of everything so we can take that out as well!

$3 x \left(3 {y}^{2} - 8 y + 5\right)$

Both 3 and 5 are prime number so we can only use 1 and themselves as whole number factors. Factors of $5 \to \left\{1 , 5\right\}$
Factors of $3 \to \left\{1 , 3\right\}$. So it a matter of experimenting with the order to see if we can reproduce $3 {y}^{2} - 8 y + 5$

Strait off there is no choice other than (3y+?)(y+?) to give $3 {y}^{2}$

$3 x \left(3 y - 5\right) \left(y - 1\right)$