# How do you factor 15x^4-39x^3+18x^2?

Jul 25, 2017

$= 3 {x}^{2} \left(x - 2\right) \left(5 x - 3\right)$

#### Explanation:

Take out a common factor of $3 {x}^{2}$ first:

$15 {x}^{4} - 39 {x}^{3} + 18 {x}^{2}$

$= 3 {x}^{2} \left(5 {x}^{2} - 13 x + 6\right)$

Find factors of $5 \mathmr{and} 6$ whose products ADD to $13$

$\text{ "5" and } 6$
$\text{ } \downarrow \textcolor{w h i t e}{\times \times} \downarrow$

$\text{ "1 color(white)(xxxxx)2" } \rightarrow 5 \times 2 = 10$
$\text{ "5color(white)(xxxxx)3" } \rightarrow 1 \times 3 = \underline{3}$
$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times \times x} 13$

These are the correct factors: the signs in both brackets will be $-$

$= 3 {x}^{2} \left(5 {x}^{2} - 13 x + 6\right)$

$= 3 {x}^{2} \left(x - 2\right) \left(5 x - 3\right)$