Simplify (2x^3-12x^2+18x-108)/(x-6)

$\frac{2 x^{3} - 12 x^{2} + 18 x - 108}{x - 6}$

Step 1

Simplify the numerator.

Factor $2$ out of $2 x^{3} - 12 x^{2} + 18 x - 108$ .

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

$\frac{2 (x^{3}) - 12 x^{2} + 18 x - 108}{x - 6}$

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

$\frac{2 (x^{3}) + 2 (- 6 x^{2}) + 18 x - 108}{x - 6}$

Factor $2$ out of $18 x$ .

$\frac{2 (x^{3}) + 2 (- 6 x^{2}) + 2 (9 x) - 108}{x - 6}$

Factor $2$ out of $- 108$ .

$\frac{2 x^{3} + 2 (- 6 x^{2}) + 2 (9 x) + 2 \cdot - 54}{x - 6}$

Factor $2$ out of $2 x^{3} + 2 (- 6 x^{2})$ .

$\frac{2 (x^{3} - 6 x^{2}) + 2 (9 x) + 2 \cdot - 54}{x - 6}$

Factor $2$ out of $2 (x^{3} - 6 x^{2}) + 2 (9 x)$ .

$\frac{2 (x^{3} - 6 x^{2} + 9 x) + 2 \cdot - 54}{x - 6}$

Factor $2$ out of $2 (x^{3} - 6 x^{2} + 9 x) + 2 \cdot - 54$ .

$\frac{2 (x^{3} - 6 x^{2} + 9 x - 54)}{x - 6}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{2 ((x^{3} - 6 x^{2}) + 9 x - 54)}{x - 6}$

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

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

Factor the polynomial by factoring out the greatest common factor, $x - 6$ .

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

Step 2

Simplify terms.

Cancel the common factor of $x - 6$ .

Cancel the common factor.

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

Divide $2 (x^{2} + 9)$ by $1$ .

$2 (x^{2} + 9)$

Apply the distributive property.

$2 x^{2} + 2 \cdot 9$

Multiply $2$ by $9$ .

$2 x^{2} + 18$