Pre-Algebra Examples

$(45 x^{7} - 30 x^{6} + 15 x^{3}) \div 5 x^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{45 x^{7} - 30 x^{6} + 15 x^{3}}{5 x^{3}}$

Step 2

Factor $15 x^{3}$ out of $45 x^{7} - 30 x^{6} + 15 x^{3}$ .

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Step 2.1

Factor $15 x^{3}$ out of $45 x^{7}$ .

$\frac{15 x^{3} (3 x^{4}) - 30 x^{6} + 15 x^{3}}{5 x^{3}}$

Step 2.2

Factor $15 x^{3}$ out of $- 30 x^{6}$ .

$\frac{15 x^{3} (3 x^{4}) + 15 x^{3} (- 2 x^{3}) + 15 x^{3}}{5 x^{3}}$

Step 2.3

Factor $15 x^{3}$ out of $15 x^{3}$ .

$\frac{15 x^{3} (3 x^{4}) + 15 x^{3} (- 2 x^{3}) + 15 x^{3} (1)}{5 x^{3}}$

Step 2.4

Factor $15 x^{3}$ out of $15 x^{3} (3 x^{4}) + 15 x^{3} (- 2 x^{3})$ .

$\frac{15 x^{3} (3 x^{4} - 2 x^{3}) + 15 x^{3} (1)}{5 x^{3}}$

Step 2.5

Factor $15 x^{3}$ out of $15 x^{3} (3 x^{4} - 2 x^{3}) + 15 x^{3} (1)$ .

$\frac{15 x^{3} (3 x^{4} - 2 x^{3} + 1)}{5 x^{3}}$

Step 3

Cancel the common factor of $15$ and $5$ .

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Step 3.1

Factor $5$ out of $15 x^{3} (3 x^{4} - 2 x^{3} + 1)$ .

$\frac{5 (3 x^{3} (3 x^{4} - 2 x^{3} + 1))}{5 x^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{5 (3 x^{3} (3 x^{4} - 2 x^{3} + 1))}{5 (x^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (3 x^{3} (3 x^{4} - 2 x^{3} + 1))}{5 x^{3}}$

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

Cancel the common factor.

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

Step 4.2

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

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

Step 5

Apply the distributive property.

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

Step 6

Simplify.

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Step 6.1

Multiply $3$ by $3$ .

$9 x^{4} + 3 (- 2 x^{3}) + 3 \cdot 1$

Step 6.2

Multiply $- 2$ by $3$ .

$9 x^{4} - 6 x^{3} + 3 \cdot 1$

Step 6.3

Multiply $3$ by $1$ .

$9 x^{4} - 6 x^{3} + 3$