Solve Q(x)*r(x)=5-3x^3+2+8x^2

$$Q(x) \times r(x) = 5-3 { x }^{ 3 } +2+8 { x }^{ 2 }$$

Solve for Q

$$\left\{\begin{matrix}Q=\frac{7+8x^{2}-3x^{3}}{rx^{2}}\text{, }&x\neq 0\text{ and }r\neq 0\\Q\in \mathrm{R}\text{, }&x=\sqrt[3]{\frac{\sqrt{78729}}{162}+\frac{2725}{1458}}+\sqrt[3]{-\frac{\sqrt{78729}}{162}+\frac{2725}{1458}}+\frac{8}{9}\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$Qx^{2}r=5-3x^{3}+2+8x^{2}$$

Add 5 and 2 to get 7.

$$Qx^{2}r=7-3x^{3}+8x^{2}$$

The equation is in standard form.

$$rx^{2}Q=7+8x^{2}-3x^{3}$$

Divide both sides by x^{2}r.

$$\frac{rx^{2}Q}{rx^{2}}=\frac{7+8x^{2}-3x^{3}}{rx^{2}}$$

Dividing by x^{2}r undoes the multiplication by x^{2}r.

$$Q=\frac{7+8x^{2}-3x^{3}}{rx^{2}}$$

Solve for r

$$\left\{\begin{matrix}r=\frac{7+8x^{2}-3x^{3}}{Qx^{2}}\text{, }&x\neq 0\text{ and }Q\neq 0\\r\in \mathrm{R}\text{, }&x=\sqrt[3]{\frac{\sqrt{78729}}{162}+\frac{2725}{1458}}+\sqrt[3]{-\frac{\sqrt{78729}}{162}+\frac{2725}{1458}}+\frac{8}{9}\text{ and }Q=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$Qx^{2}r=5-3x^{3}+2+8x^{2}$$

Add 5 and 2 to get 7.

$$Qx^{2}r=7-3x^{3}+8x^{2}$$

The equation is in standard form.

$$Qx^{2}r=7+8x^{2}-3x^{3}$$

Divide both sides by Qx^{2}.

$$\frac{Qx^{2}r}{Qx^{2}}=\frac{7+8x^{2}-3x^{3}}{Qx^{2}}$$

Dividing by Qx^{2} undoes the multiplication by Qx^{2}.

$$r=\frac{7+8x^{2}-3x^{3}}{Qx^{2}}$$