How do you factor $3 x^{3} - 300 x$ $3x^3-300x$ ?

Question

3019 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-18T01:51:57

First, let's factor out what both elements share: $3 x$ $3x$

$3 x (x^{2} - 100)$ $3x(x^2-100)$

Now, we can factor the quadratic inside the parenthesis by finding its roots and then turning them into factors:

$x^{2} = 100$ $x^2=100$
$x = \sqrt{100}$ $x=sqrt(100)$
$x = \pm 10$ $x=+-10$

$x = 10$ $x=10$ can be rewritten as $x - 10 = 0$ $x-10=0$
$x = - 10$ $x=-10$ can be rewritten as $x + 10 = 0$ $x+10=0$

So, rewriting our factors, we have

$3 x (x - 10) (x + 10)$ $3x(x-10)(x+10)$

How do you factor 3x3−300x3x^3-300x?