Pre-Algebra Examples

$(- 12 x^{8} + x^{6} - 8 x^{3}) \div 4 x^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{- 12 x^{8} + x^{6} - 8 x^{3}}{4 x^{2}}$

Step 2

Factor $x^{3}$ out of $- 12 x^{8} + x^{6} - 8 x^{3}$ .

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Step 2.1

Factor $x^{3}$ out of $- 12 x^{8}$ .

$\frac{x^{3} (- 12 x^{5}) + x^{6} - 8 x^{3}}{4 x^{2}}$

Step 2.2

Factor $x^{3}$ out of $x^{6}$ .

$\frac{x^{3} (- 12 x^{5}) + x^{3} x^{3} - 8 x^{3}}{4 x^{2}}$

Step 2.3

Factor $x^{3}$ out of $- 8 x^{3}$ .

$\frac{x^{3} (- 12 x^{5}) + x^{3} x^{3} + x^{3} \cdot - 8}{4 x^{2}}$

Step 2.4

Factor $x^{3}$ out of $x^{3} (- 12 x^{5}) + x^{3} x^{3}$ .

$\frac{x^{3} (- 12 x^{5} + x^{3}) + x^{3} \cdot - 8}{4 x^{2}}$

Step 2.5

Factor $x^{3}$ out of $x^{3} (- 12 x^{5} + x^{3}) + x^{3} \cdot - 8$ .

$\frac{x^{3} (- 12 x^{5} + x^{3} - 8)}{4 x^{2}}$

Step 3

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 3.1

Factor $x^{2}$ out of $x^{3} (- 12 x^{5} + x^{3} - 8)$ .

$\frac{x^{2} (x (- 12 x^{5} + x^{3} - 8))}{4 x^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{x^{2} (x (- 12 x^{5} + x^{3} - 8))}{x^{2} \cdot 4}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{2} (x (- 12 x^{5} + x^{3} - 8))}{x^{2} \cdot 4}$

Step 3.2.3

Rewrite the expression.

$\frac{x (- 12 x^{5} + x^{3} - 8)}{4}$

Step 4

Factor $- 1$ out of $- 12 x^{5}$ .

$\frac{x (- (12 x^{5}) + x^{3} - 8)}{4}$

Step 5

Factor $- 1$ out of $x^{3}$ .

$\frac{x (- (12 x^{5}) - 1 (- x^{3}) - 8)}{4}$

Step 6

Factor $- 1$ out of $- (12 x^{5}) - 1 (- x^{3})$ .

$\frac{x (- (12 x^{5} - x^{3}) - 8)}{4}$

Step 7

Rewrite $- 8$ as $- 1 (8)$ .

$\frac{x (- (12 x^{5} - x^{3}) - 1 (8))}{4}$

Step 8

Factor $- 1$ out of $- (12 x^{5} - x^{3}) - 1 (8)$ .

$\frac{x (- (12 x^{5} - x^{3} + 8))}{4}$

Step 9

Simplify the expression.

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Step 9.1

Rewrite $- (12 x^{5} - x^{3} + 8)$ as $- 1 (12 x^{5} - x^{3} + 8)$ .

$\frac{x (- 1 (12 x^{5} - x^{3} + 8))}{4}$

Step 9.2

Move the negative in front of the fraction.

$- \frac{x (12 x^{5} - x^{3} + 8)}{4}$