Factor 9x^2-20-x^4

$9 x^{2} - 20 - x^{4}$

Factor $- 1$ out of $9 x^{2} - 20 - x^{4}$ .

Reorder the expression.

Move $- 20$ .

$9 x^{2} - x^{4} - 20$

Reorder $9 x^{2}$ and $- x^{4}$ .

$- x^{4} + 9 x^{2} - 20$

Factor $- 1$ out of $- x^{4}$ .

$- (x^{4}) + 9 x^{2} - 20$

Factor $- 1$ out of $9 x^{2}$ .

$- (x^{4}) - (- 9 x^{2}) - 20$

Rewrite $- 20$ as $- 1 (20)$ .

$- (x^{4}) - (- 9 x^{2}) - 1 (20)$

Factor $- 1$ out of $- (x^{4}) - (- 9 x^{2})$ .

$- (x^{4} - 9 x^{2}) - 1 (20)$

Factor $- 1$ out of $- (x^{4} - 9 x^{2}) - 1 (20)$ .

$- (x^{4} - 9 x^{2} + 20)$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$- ({(x^{2})}^{2} - 9 x^{2} + 20)$

Let $u = x^{2}$ . Substitute $u$ for all occurrences of $x^{2}$ .

$- (u^{2} - 9 u + 20)$

Factor $u^{2} - 9 u + 20$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $20$ and whose sum is $- 9$ .

$- 5, - 4$

Write the factored form using these integers.

$- ((u - 5) (u - 4))$

Replace all occurrences of $u$ with $x^{2}$ .

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

Rewrite $4$ as $2^{2}$ .

$- ((x^{2} - 5) (x^{2} - 2^{2}))$

Factor.

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 $b = 2$ .

$- ((x^{2} - 5) ((x + 2) (x - 2)))$

Remove unnecessary parentheses.

$- ((x^{2} - 5) (x + 2) (x - 2))$

Remove unnecessary parentheses.

$- (x^{2} - 5) (x + 2) (x - 2)$

Factor 9x^2-20-x^4

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