Divide (-2x^3-3x^2-4x+12)/(4x)

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

Step 1

Factor $- 1$ out of $- 2 x^{3}$ .

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

Step 2

Factor $- 1$ out of $- 3 x^{2}$ .

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

Step 3

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

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

Step 4

Factor $- 1$ out of $- 4 x$ .

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

Step 5

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

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

Step 6

Rewrite $12$ as $- 1 (- 12)$ .

$\frac{- (2 x^{3} + 3 x^{2} + 4 x) - 1 (- 12)}{4 x}$

Step 7

Factor $- 1$ out of $- (2 x^{3} + 3 x^{2} + 4 x) - 1 (- 12)$ .

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

Step 8

Rewrite $- (2 x^{3} + 3 x^{2} + 4 x - 12)$ as $- 1 (2 x^{3} + 3 x^{2} + 4 x - 12)$ .

$\frac{- 1 (2 x^{3} + 3 x^{2} + 4 x - 12)}{4 x}$

Step 9

Move the negative in front of the fraction.

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

Step 10

Split the fraction $\frac{2 x^{3} + 3 x^{2} + 4 x - 12}{4 x}$ into two fractions.

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

Step 11

Split the fraction $\frac{2 x^{3} + 3 x^{2} + 4 x}{4 x}$ into two fractions.

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

Step 12

Split the fraction $\frac{2 x^{3} + 3 x^{2}}{4 x}$ into two fractions.

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

Step 13

Cancel the common factor of $2$ and $4$ .

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

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

Cancel the common factors.

Factor $2$ out of $4 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 14

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

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

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

Cancel the common factors.

Factor $x$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 15

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

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

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

Cancel the common factors.

Factor $x$ out of $4 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 16

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 17

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

$- (\frac{x^{2}}{2} + \frac{3 x}{4} + 1 + \frac{- 12}{4 x})$

Step 18

Cancel the common factor of $- 12$ and $4$ .

Factor $4$ out of $- 12$ .

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

Cancel the common factors.

Factor $4$ out of $4 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 19

Move the negative in front of the fraction.

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

Divide (-2x^3-3x^2-4x+12)/(4x)

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