Pre-Algebra Examples

$\frac{8 x^{7} - 6 x^{5} + 10 x^{2}}{- 2 x^{2}}$

Step 1

Factor $2 x^{2}$ out of $8 x^{7} - 6 x^{5} + 10 x^{2}$ .

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Step 1.1

Factor $2 x^{2}$ out of $8 x^{7}$ .

$\frac{2 x^{2} (4 x^{5}) - 6 x^{5} + 10 x^{2}}{- 2 x^{2}}$

Step 1.2

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

$\frac{2 x^{2} (4 x^{5}) + 2 x^{2} (- 3 x^{3}) + 10 x^{2}}{- 2 x^{2}}$

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Cancel the common factor of $2$ and $- 2$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{4 x^{5} - 3 x^{3} + 5}{- 1}$

Step 3.3

Move the negative one from the denominator of $\frac{4 x^{5} - 3 x^{3} + 5}{- 1}$ .

$- 1 \cdot (4 x^{5} - 3 x^{3} + 5)$

Step 4

Rewrite $- 1 \cdot (4 x^{5} - 3 x^{3} + 5)$ as $- (4 x^{5} - 3 x^{3} + 5)$ .

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

Step 5

Apply the distributive property.

$- (4 x^{5}) - (- 3 x^{3}) - 1 \cdot 5$

Step 6

Simplify.

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Step 6.1

Multiply $4$ by $- 1$ .

$- 4 x^{5} - (- 3 x^{3}) - 1 \cdot 5$

Step 6.2

Multiply $- 3$ by $- 1$ .

$- 4 x^{5} + 3 x^{3} - 1 \cdot 5$

Step 6.3

Multiply $- 1$ by $5$ .

$- 4 x^{5} + 3 x^{3} - 5$