Algebra Examples

$(10 x^{6} + 20 x^{4} - 15 x^{2}) \div 5 x^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{10 x^{6} + 20 x^{4} - 15 x^{2}}{5 x^{2}}$

Step 2

Factor $5 x^{2}$ out of $10 x^{6} + 20 x^{4} - 15 x^{2}$ .

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Step 2.1

Factor $5 x^{2}$ out of $10 x^{6}$ .

$\frac{5 x^{2} (2 x^{4}) + 20 x^{4} - 15 x^{2}}{5 x^{2}}$

Step 2.2

Factor $5 x^{2}$ out of $20 x^{4}$ .

$\frac{5 x^{2} (2 x^{4}) + 5 x^{2} (4 x^{2}) - 15 x^{2}}{5 x^{2}}$

Step 2.3

Factor $5 x^{2}$ out of $- 15 x^{2}$ .

$\frac{5 x^{2} (2 x^{4}) + 5 x^{2} (4 x^{2}) + 5 x^{2} (- 3)}{5 x^{2}}$

Step 2.4

Factor $5 x^{2}$ out of $5 x^{2} (2 x^{4}) + 5 x^{2} (4 x^{2})$ .

$\frac{5 x^{2} (2 x^{4} + 4 x^{2}) + 5 x^{2} (- 3)}{5 x^{2}}$

Step 2.5

Factor $5 x^{2}$ out of $5 x^{2} (2 x^{4} + 4 x^{2}) + 5 x^{2} (- 3)$ .

$\frac{5 x^{2} (2 x^{4} + 4 x^{2} - 3)}{5 x^{2}}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\frac{5 x^{2} (2 x^{4} + 4 x^{2} - 3)}{5 x^{2}}$

Step 3.2

Rewrite the expression.

$\frac{x^{2} (2 x^{4} + 4 x^{2} - 3)}{x^{2}}$

Step 4

Cancel the common factor of $x^{2}$ .

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Step 4.1

Cancel the common factor.

$\frac{x^{2} (2 x^{4} + 4 x^{2} - 3)}{x^{2}}$

Step 4.2

Divide $2 x^{4} + 4 x^{2} - 3$ by $1$ .

$2 x^{4} + 4 x^{2} - 3$