# How do you factor by grouping x^3+6x^2-5x-30?

Jun 8, 2015

${x}^{3} + 6 {x}^{2} - 5 x - 30$

$= \left({x}^{3} + 6 {x}^{2}\right) - \left(5 x + 30\right)$

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

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

If you allow irrational coefficients...

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

$= \left(x - \sqrt{5}\right) \left(x + \sqrt{5}\right) \left(x + 6\right)$

..using the difference of squares identity:

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