Factor polynomial $$ x^{6}-2x^{4}-25x^{2}+50 $$

$$ x^{6}-2x^{4}-25x^{2}+50 = ( x^{2}-5 )( x^{2}+5 )( x^{2}-2 ) $$

Step 1 :

To factor $ x^{6}-2x^{4}-25x^{2}+50 $ we can use factoring by grouping:

Group $ \color{blue}{ x^{6} }$ with $ \color{blue}{ -2x^{4} }$ and $ \color{red}{ -25x^{2} }$ with $ \color{red}{ 50 }$ then factor each group.

$$ \begin{aligned} x^{6}-2x^{4}-25x^{2}+50 = ( \color{blue}{ x^{6}-2x^{4} } ) + ( \color{red}{ -25x^{2}+50 }) &= \\ &= \color{blue}{ x^{4}( x^{2}-2 )} + \color{red}{ -25( x^{2}-2 ) } = \\ &= (x^{4}-25)(x^{2}-2) \end{aligned} $$

Step 2 :

Rewrite $ x^{4}-25 $ as:

$$ x^{4}-25 = (x^{2})^2 - (5)^2 $$

Now we can apply the difference of squares formula.

$$ I^2 - II^2 = (I - II)(I + II) $$

After putting $ I = x^{2} $ and $ II = 5 $ , we have:

$$ x^{4}-25 = (x^{2})^2 - (5)^2 = ( x^{2}-5 ) ( x^{2}+5 ) $$

Polynomial Factoring Calculator