Divide (36x^3-96x^2+48x)/(12x)

$\frac{36 x^{3} - 96 x^{2} + 48 x}{12 x}$

Step 1

Simplify the numerator.

Factor $12 x$ out of $36 x^{3} - 96 x^{2} + 48 x$ .

Factor $12 x$ out of $36 x^{3}$ .

$\frac{12 x (3 x^{2}) - 96 x^{2} + 48 x}{12 x}$

Factor $12 x$ out of $- 96 x^{2}$ .

$\frac{12 x (3 x^{2}) + 12 x (- 8 x) + 48 x}{12 x}$

Factor $12 x$ out of $48 x$ .

$\frac{12 x (3 x^{2}) + 12 x (- 8 x) + 12 x (4)}{12 x}$

Factor $12 x$ out of $12 x (3 x^{2}) + 12 x (- 8 x)$ .

$\frac{12 x (3 x^{2} - 8 x) + 12 x (4)}{12 x}$

Factor $12 x$ out of $12 x (3 x^{2} - 8 x) + 12 x (4)$ .

$\frac{12 x (3 x^{2} - 8 x + 4)}{12 x}$

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 $a \cdot c = 3 \cdot 4 = 12$ and whose sum is $b = - 8$ .

Factor $- 8$ out of $- 8 x$ .

$\frac{12 x (3 x^{2} - 8 (x) + 4)}{12 x}$

Rewrite $- 8$ as $- 2$ plus $- 6$

$\frac{12 x (3 x^{2} + (- 2 - 6) x + 4)}{12 x}$

Apply the distributive property.

$\frac{12 x (3 x^{2} - 2 x - 6 x + 4)}{12 x}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{12 x ((3 x^{2} - 2 x) - 6 x + 4)}{12 x}$

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

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

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

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

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

Step 2

Cancel the common factor of $12$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x$ .

Cancel the common factor.

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

Divide $(3 x - 2) (x - 2)$ by $1$ .

$(3 x - 2) (x - 2)$

Step 4

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

Apply the distributive property.

$3 x (x - 2) - 2 (x - 2)$

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 2 - 2 (x - 2)$

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 2 - 2 x - 2 \cdot - 2$

Step 5

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$3 (x \cdot x) + 3 x \cdot - 2 - 2 x - 2 \cdot - 2$

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $3$ .

$3 x^{2} - 6 x - 2 x - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$3 x^{2} - 6 x - 2 x + 4$

Subtract $2 x$ from $- 6 x$ .

$3 x^{2} - 8 x + 4$

Divide (36x^3-96x^2+48x)/(12x)

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