Calculus Examples

$- \frac{1}{256} x^{8} + \frac{1}{16} x^{6} - \frac{3}{8} x^{4} + x^{2}$

Step 1

Factor $x^{2}$ out of $- \frac{1}{256} x^{8} + \frac{1}{16} x^{6} - \frac{3}{8} x^{4} + x^{2}$ .

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Step 1.1

Factor $x^{2}$ out of $- \frac{1}{256} x^{8}$ .

$x^{2} (- \frac{1}{256} x^{6}) + \frac{1}{16} x^{6} - \frac{3}{8} x^{4} + x^{2}$

Step 1.2

Factor $x^{2}$ out of $\frac{1}{16} x^{6}$ .

$x^{2} (- \frac{1}{256} x^{6}) + x^{2} (\frac{1}{16} x^{4}) - \frac{3}{8} x^{4} + x^{2}$

Step 1.3

Factor $x^{2}$ out of $- \frac{3}{8} x^{4}$ .

$x^{2} (- \frac{1}{256} x^{6}) + x^{2} (\frac{1}{16} x^{4}) + x^{2} (- \frac{3}{8} x^{2}) + x^{2}$

Step 1.4

Multiply by $1$ .

$x^{2} (- \frac{1}{256} x^{6}) + x^{2} (\frac{1}{16} x^{4}) + x^{2} (- \frac{3}{8} x^{2}) + x^{2} \cdot 1$

Step 1.5

Factor $x^{2}$ out of $x^{2} (- \frac{1}{256} x^{6}) + x^{2} (\frac{1}{16} x^{4})$ .

$x^{2} (- \frac{1}{256} x^{6} + \frac{1}{16} x^{4}) + x^{2} (- \frac{3}{8} x^{2}) + x^{2} \cdot 1$

Step 1.6

Factor $x^{2}$ out of $x^{2} (- \frac{1}{256} x^{6} + \frac{1}{16} x^{4}) + x^{2} (- \frac{3}{8} x^{2})$ .

$x^{2} (- \frac{1}{256} x^{6} + \frac{1}{16} x^{4} - \frac{3}{8} x^{2}) + x^{2} \cdot 1$

Step 1.7

Factor $x^{2}$ out of $x^{2} (- \frac{1}{256} x^{6} + \frac{1}{16} x^{4} - \frac{3}{8} x^{2}) + x^{2} \cdot 1$ .

$x^{2} (- \frac{1}{256} x^{6} + \frac{1}{16} x^{4} - \frac{3}{8} x^{2} + 1)$

Step 2

Factor.

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Step 2.1

Factor $\frac{1}{256}$ out of each term.

$x^{2} (\frac{1}{256} (- 1 x^{6} + 16 x^{4} - 96 x^{2} + 256))$

Step 2.2

Remove unnecessary parentheses.

$x^{2} \frac{1}{256} (- 1 x^{6} + 16 x^{4} - 96 x^{2} + 256)$

Step 3

Combine $x^{2}$ and $\frac{1}{256}$ .

$\frac{x^{2}}{256} (- 1 x^{6} + 16 x^{4} - 96 x^{2} + 256)$

Step 4

Rewrite $- 1 x^{6}$ as $- x^{6}$ .

$\frac{x^{2}}{256} \cdot (- x^{6} + 16 x^{4} - 96 x^{2} + 256)$