Pre-Algebra Examples

$(3 x^{3} - 2 x^{2} - 1) \div x^{2}$

Step 1

Rewrite the division as a fraction.

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

Step 2

Split the fraction $\frac{3 x^{3} - 2 x^{2} - 1}{x^{2}}$ into two fractions.

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 4.2.4

Divide $3 x$ by $1$ .

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $- 2$ by $1$ .

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

Step 6

Move the negative in front of the fraction.

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