Factor 13x^2-42-x^4

$13 x^{2} - 42 - x^{4}$

Step 1

Factor $- 1$ out of $13 x^{2} - 42 - x^{4}$ .

Reorder the expression.

Move $- 42$ .

$13 x^{2} - x^{4} - 42$

Reorder $13 x^{2}$ and $- x^{4}$ .

$- x^{4} + 13 x^{2} - 42$

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

$- (x^{4}) + 13 x^{2} - 42$

Factor $- 1$ out of $13 x^{2}$ .

$- (x^{4}) - (- 13 x^{2}) - 42$

Rewrite $- 42$ as $- 1 (42)$ .

$- (x^{4}) - (- 13 x^{2}) - 1 (42)$

Factor $- 1$ out of $- (x^{4}) - (- 13 x^{2})$ .

$- (x^{4} - 13 x^{2}) - 1 (42)$

Factor $- 1$ out of $- (x^{4} - 13 x^{2}) - 1 (42)$ .

$- (x^{4} - 13 x^{2} + 42)$

Step 2

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

$- ({(x^{2})}^{2} - 13 x^{2} + 42)$

Step 3

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

$- (u^{2} - 13 u + 42)$

Step 4

Factor $u^{2} - 13 u + 42$ 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 $42$ and whose sum is $- 13$ .

$- 7, - 6$

Write the factored form using these integers.

$- ((u - 7) (u - 6))$

Step 5

Factor.

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

$- ((x^{2} - 7) (x^{2} - 6))$

Remove unnecessary parentheses.

$- (x^{2} - 7) (x^{2} - 6)$

Factor 13x^2-42-x^4

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