Trigonometry Examples

$f (x) = \frac{1}{4} x^{4} - 2 x^{2}$

Step 1

Factor $x^{2}$ out of $\frac{1}{4} x^{4} - 2 x^{2}$ .

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Step 1.1

Factor $x^{2}$ out of $\frac{1}{4} x^{4}$ .

$f (x) = x^{2} (\frac{1}{4} x^{2}) - 2 x^{2}$

Step 1.2

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

$f (x) = x^{2} (\frac{1}{4} x^{2}) + x^{2} \cdot - 2$

Step 1.3

Factor $x^{2}$ out of $x^{2} (\frac{1}{4} x^{2}) + x^{2} \cdot - 2$ .

$f (x) = x^{2} (\frac{1}{4} x^{2} - 2)$

Step 2

Factor.

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Step 2.1

Factor $\frac{1}{4}$ out of each term.

$f (x) = x^{2} (\frac{1}{4} \cdot (x^{2} - 8))$

Step 2.2

Remove unnecessary parentheses.

$f (x) = x^{2} (\frac{1}{4}) \cdot (x^{2} - 8)$

Step 3

Combine $x^{2}$ and $\frac{1}{4}$ .

$f (x) = \frac{x^{2}}{4} \cdot (x^{2} - 8)$