# How do you factor 256x^2 - 49?

May 21, 2015

You can find its roots and then turn them into factors:

$256 {x}^{2} - 49$
${x}^{2} = \frac{49}{256}$
$x = \sqrt{\frac{49}{256}}$
$x = \pm \left(\frac{7}{16}\right)$

Transforming each root $x = \pm \frac{7}{16}$ into factors...

$16 x - 7 = 0$ and $16 x + 7 = 0$

So, $256 {x}^{2} - 49 = \textcolor{g r e e n}{\left(16 x - 7\right) \left(16 x + 7\right)}$