Pre-Algebra Examples

$(48 x^{5} - 24 x^{3} + 9 x^{2}) \div 6 x^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{48 x^{5} - 24 x^{3} + 9 x^{2}}{6 x^{2}}$

Step 2

Factor $3 x^{2}$ out of $48 x^{5} - 24 x^{3} + 9 x^{2}$ .

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Step 2.1

Factor $3 x^{2}$ out of $48 x^{5}$ .

$\frac{3 x^{2} (16 x^{3}) - 24 x^{3} + 9 x^{2}}{6 x^{2}}$

Step 2.2

Factor $3 x^{2}$ out of $- 24 x^{3}$ .

$\frac{3 x^{2} (16 x^{3}) + 3 x^{2} (- 8 x) + 9 x^{2}}{6 x^{2}}$

Step 2.3

Factor $3 x^{2}$ out of $9 x^{2}$ .

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

Step 2.4

Factor $3 x^{2}$ out of $3 x^{2} (16 x^{3}) + 3 x^{2} (- 8 x)$ .

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

Step 2.5

Factor $3 x^{2}$ out of $3 x^{2} (16 x^{3} - 8 x) + 3 x^{2} (3)$ .

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

Step 3

Cancel the common factor of $3$ and $6$ .

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Step 3.1

Factor $3$ out of $3 x^{2} (16 x^{3} - 8 x + 3)$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $6 x^{2}$ .

$\frac{3 (x^{2} (16 x^{3} - 8 x + 3))}{3 (2 x^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (x^{2} (16 x^{3} - 8 x + 3))}{3 (2 x^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{2} (16 x^{3} - 8 x + 3)}{2 x^{2}}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{x^{2} (16 x^{3} - 8 x + 3)}{2 x^{2}}$

Step 4.2

Rewrite the expression.

$\frac{16 x^{3} - 8 x + 3}{2}$

Step 5

Split the fraction $\frac{16 x^{3} - 8 x + 3}{2}$ into two fractions.

$\frac{16 x^{3} - 8 x}{2} + \frac{3}{2}$

Step 6

Split the fraction $\frac{16 x^{3} - 8 x}{2}$ into two fractions.

$\frac{16 x^{3}}{2} + \frac{- 8 x}{2} + \frac{3}{2}$

Step 7

Cancel the common factor of $16$ and $2$ .

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Step 7.1

Factor $2$ out of $16 x^{3}$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $2$ .

$\frac{2 (8 x^{3})}{2 (1)} + \frac{- 8 x}{2} + \frac{3}{2}$

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 7.2.4

Divide $8 x^{3}$ by $1$ .

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

Step 8

Cancel the common factor of $- 8$ and $2$ .

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Step 8.1

Factor $2$ out of $- 8 x$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $2$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 8.2.4

Divide $- 4 x$ by $1$ .

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