# How do you factor 56x^3+70x^2-280x-350?

Apr 26, 2016

$56 {x}^{3} + 70 {x}^{2} - 280 x - 350 = 14 \left(x - \sqrt{5}\right) \left(x + \sqrt{5}\right) \left(4 x + 5\right)$

#### Explanation:

Separate out the common scalar factor $14$, factor by grouping and finally use the difference of squares identity:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

with $a = x$ and $b = \sqrt{5}$ as follows:

$56 {x}^{3} + 70 {x}^{2} - 280 x - 350$

$= 14 \left(4 {x}^{3} + 5 {x}^{2} - 20 x - 25\right)$

$= 14 \left(\left(4 {x}^{3} + 5 {x}^{2}\right) - \left(20 x + 25\right)\right)$

$= 14 \left({x}^{2} \left(4 x + 5\right) - 5 \left(4 x + 5\right)\right)$

$= 14 \left({x}^{2} - 5\right) \left(4 x + 5\right)$

$= 14 \left({x}^{2} - {\left(\sqrt{5}\right)}^{2}\right) \left(4 x + 5\right)$

$= 14 \left(x - \sqrt{5}\right) \left(x + \sqrt{5}\right) \left(4 x + 5\right)$