Write in Standard Form (6x^2-9x^3+3)/3

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Cancel the common factor of $6 x^{2} - 9 x^{3} + 3$ and $3$ .

Factor $3$ out of $6 x^{2}$ .

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

Factor $3$ out of $- 9 x^{3}$ .

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

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

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

Factor $3$ out of $3$ .

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

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

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 x^{2} - 3 x^{3} + 1$ by $1$ .

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

Step 3

Reorder $2 x^{2}$ and $- 3 x^{3}$ .

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