Divide (12x^2-4x-8)/(4x)

$\frac{12 x^{2} - 4 x - 8}{4 x}$

Step 1

Cancel the common factor of $12 x^{2} - 4 x - 8$ and $4$ .

Factor $4$ out of $12 x^{2}$ .

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

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

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

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

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

Factor $4$ out of $- 8$ .

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

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

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

Cancel the common factors.

Factor $4$ out of $4 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 2 = - 6$ and whose sum is $b = - 1$ .

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

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

Rewrite $- 1$ as $2$ plus $- 3$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $3 x + 2$ .

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

Step 3

Expand $(3 x + 2) (x - 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 4

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $3$ .

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

Multiply $2$ by $- 1$ .

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

Add $- 3 x$ and $2 x$ .

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

Step 5

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

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

Step 6

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

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

Step 7

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

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

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

Cancel the common factors.

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3 x$ by $1$ .

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

Step 8

Cancel the common factor of $x$ .

Cancel the common factor.

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

Divide $- 1$ by $1$ .

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

Step 9

Move the negative in front of the fraction.

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

Divide (12x^2-4x-8)/(4x)

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