Factor by Grouping x^6-x^4-2x^2+2

$x^{6} - x^{4} - 2 x^{2} + 2$

Step 1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{6} - x^{4}) - 2 x^{2} + 2$

Factor out the greatest common factor (GCF) from each group.

$x^{4} (x^{2} - 1) - 2 (x^{2} - 1)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $x^{2} - 1$ .

$(x^{2} - 1) (x^{4} - 2)$

Step 3

Rewrite $1$ as $1^{2}$ .

$(x^{2} - 1^{2}) (x^{4} - 2)$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$(x + 1) (x - 1) (x^{4} - 2)$