Pre-Algebra Examples

$(40 x^{7} - 64 x^{6} - 24 x^{4}) \div (- 8 x^{4})$

Step 1

Rewrite the division as a fraction.

$\frac{40 x^{7} - 64 x^{6} - 24 x^{4}}{- 8 x^{4}}$

Step 2

Factor $8 x^{4}$ out of $40 x^{7} - 64 x^{6} - 24 x^{4}$ .

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Step 2.1

Factor $8 x^{4}$ out of $40 x^{7}$ .

$\frac{8 x^{4} (5 x^{3}) - 64 x^{6} - 24 x^{4}}{- 8 x^{4}}$

Step 2.2

Factor $8 x^{4}$ out of $- 64 x^{6}$ .

$\frac{8 x^{4} (5 x^{3}) + 8 x^{4} (- 8 x^{2}) - 24 x^{4}}{- 8 x^{4}}$

Step 2.3

Factor $8 x^{4}$ out of $- 24 x^{4}$ .

$\frac{8 x^{4} (5 x^{3}) + 8 x^{4} (- 8 x^{2}) + 8 x^{4} (- 3)}{- 8 x^{4}}$

Step 2.4

Factor $8 x^{4}$ out of $8 x^{4} (5 x^{3}) + 8 x^{4} (- 8 x^{2})$ .

$\frac{8 x^{4} (5 x^{3} - 8 x^{2}) + 8 x^{4} (- 3)}{- 8 x^{4}}$

Step 2.5

Factor $8 x^{4}$ out of $8 x^{4} (5 x^{3} - 8 x^{2}) + 8 x^{4} (- 3)$ .

$\frac{8 x^{4} (5 x^{3} - 8 x^{2} - 3)}{- 8 x^{4}}$

Step 3

Cancel the common factor of $8$ and $- 8$ .

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Step 3.1

Factor $8$ out of $8 x^{4} (5 x^{3} - 8 x^{2} - 3)$ .

$\frac{8 (x^{4} (5 x^{3} - 8 x^{2} - 3))}{- 8 x^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $8$ out of $- 8 x^{4}$ .

$\frac{8 (x^{4} (5 x^{3} - 8 x^{2} - 3))}{8 (- x^{4})}$

Step 3.2.2

Cancel the common factor.

$\frac{8 (x^{4} (5 x^{3} - 8 x^{2} - 3))}{8 (- x^{4})}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{4} (5 x^{3} - 8 x^{2} - 3)}{- x^{4}}$

Step 4

Cancel the common factor of $x^{4}$ .

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Step 4.1

Cancel the common factor.

$\frac{x^{4} (5 x^{3} - 8 x^{2} - 3)}{- x^{4}}$

Step 4.2

Rewrite the expression.

$\frac{5 x^{3} - 8 x^{2} - 3}{- 1}$

Step 4.3

Move the negative one from the denominator of $\frac{5 x^{3} - 8 x^{2} - 3}{- 1}$ .

$- 1 \cdot (5 x^{3} - 8 x^{2} - 3)$

Step 5

Rewrite $- 1 \cdot (5 x^{3} - 8 x^{2} - 3)$ as $- (5 x^{3} - 8 x^{2} - 3)$ .

$- (5 x^{3} - 8 x^{2} - 3)$

Step 6

Apply the distributive property.

$- (5 x^{3}) - (- 8 x^{2}) - - 3$

Step 7

Simplify.

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Step 7.1

Multiply $5$ by $- 1$ .

$- 5 x^{3} - (- 8 x^{2}) - - 3$

Step 7.2

Multiply $- 8$ by $- 1$ .

$- 5 x^{3} + 8 x^{2} - - 3$

Step 7.3

Multiply $- 1$ by $- 3$ .

$- 5 x^{3} + 8 x^{2} + 3$