Algebra Examples

$- 4 x^{4} + 26 x^{2} - 30$

Step 1

Factor $- 2$ out of $- 4 x^{4} + 26 x^{2} - 30$ .

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Step 1.1

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

$- 2 (2 x^{4}) + 26 x^{2} - 30$

Step 1.2

Factor $- 2$ out of $26 x^{2}$ .

$- 2 (2 x^{4}) - 2 (- 13 x^{2}) - 30$

Step 1.3

Factor $- 2$ out of $- 30$ .

$- 2 (2 x^{4}) - 2 (- 13 x^{2}) - 2 (15)$

Step 1.4

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

$- 2 (2 x^{4} - 13 x^{2}) - 2 (15)$

Step 1.5

Factor $- 2$ out of $- 2 (2 x^{4} - 13 x^{2}) - 2 (15)$ .

$- 2 (2 x^{4} - 13 x^{2} + 15)$

Step 2

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

$- 2 (2 {(x^{2})}^{2} - 13 x^{2} + 15)$

Step 3

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

$- 2 (2 u^{2} - 13 u + 15)$

Step 4

Factor by grouping.

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Step 4.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 15 = 30$ and whose sum is $b = - 13$ .

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Step 4.1.1

Factor $- 13$ out of $- 13 u$ .

$- 2 (2 u^{2} - 13 (u) + 15)$

Step 4.1.2

Rewrite $- 13$ as $- 3$ plus $- 10$

$- 2 (2 u^{2} + (- 3 - 10) u + 15)$

Step 4.1.3

Apply the distributive property.

$- 2 (2 u^{2} - 3 u - 10 u + 15)$

Step 4.2

Factor out the greatest common factor from each group.

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Step 4.2.1

Group the first two terms and the last two terms.

$- 2 ((2 u^{2} - 3 u) - 10 u + 15)$

Step 4.2.2

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

$- 2 (u (2 u - 3) - 5 (2 u - 3))$

Step 4.3

Factor the polynomial by factoring out the greatest common factor, $2 u - 3$ .

$- 2 ((2 u - 3) (u - 5))$

Step 5

Factor.

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Step 5.1

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

$- 2 ((2 x^{2} - 3) (x^{2} - 5))$

Step 5.2

Remove unnecessary parentheses.

$- 2 (2 x^{2} - 3) (x^{2} - 5)$