Pre-Algebra Examples

$(6 x^{4} + 8 x^{3} - 18 x^{2}) \div 3 x^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{6 x^{4} + 8 x^{3} - 18 x^{2}}{3 x^{2}}$

Step 2

Factor $2 x^{2}$ out of $6 x^{4} + 8 x^{3} - 18 x^{2}$ .

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Step 2.1

Factor $2 x^{2}$ out of $6 x^{4}$ .

$\frac{2 x^{2} (3 x^{2}) + 8 x^{3} - 18 x^{2}}{3 x^{2}}$

Step 2.2

Factor $2 x^{2}$ out of $8 x^{3}$ .

$\frac{2 x^{2} (3 x^{2}) + 2 x^{2} (4 x) - 18 x^{2}}{3 x^{2}}$

Step 2.3

Factor $2 x^{2}$ out of $- 18 x^{2}$ .

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

Step 2.4

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

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

Step 2.5

Factor $2 x^{2}$ out of $2 x^{2} (3 x^{2} + 4 x) + 2 x^{2} (- 9)$ .

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

Step 3

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

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Apply the distributive property.

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

Step 5

Simplify.

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Step 5.1

Multiply $3$ by $2$ .

$\frac{6 x^{2} + 2 (4 x) + 2 \cdot - 9}{3}$

Step 5.2

Multiply $4$ by $2$ .

$\frac{6 x^{2} + 8 x + 2 \cdot - 9}{3}$

Step 5.3

Multiply $2$ by $- 9$ .

$\frac{6 x^{2} + 8 x - 18}{3}$

Step 6

Split the fraction $\frac{6 x^{2} + 8 x - 18}{3}$ into two fractions.

$\frac{6 x^{2} + 8 x}{3} + \frac{- 18}{3}$

Step 7

Split the fraction $\frac{6 x^{2} + 8 x}{3}$ into two fractions.

$\frac{6 x^{2}}{3} + \frac{8 x}{3} + \frac{- 18}{3}$

Step 8

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

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Step 8.1

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

$\frac{3 (2 x^{2})}{3} + \frac{8 x}{3} + \frac{- 18}{3}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $3$ .

$\frac{3 (2 x^{2})}{3 (1)} + \frac{8 x}{3} + \frac{- 18}{3}$

Step 8.2.2

Cancel the common factor.

$\frac{3 (2 x^{2})}{3 \cdot 1} + \frac{8 x}{3} + \frac{- 18}{3}$

Step 8.2.3

Rewrite the expression.

$\frac{2 x^{2}}{1} + \frac{8 x}{3} + \frac{- 18}{3}$

Step 8.2.4

Divide $2 x^{2}$ by $1$ .

$2 x^{2} + \frac{8 x}{3} + \frac{- 18}{3}$

Step 9

Divide $- 18$ by $3$ .

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