Solve Df(x)=(4x^3+4)(2x^4+8)=

$$D f ( x ) = ( 4 x ^ { 3 } + 4 ) ( 2 x ^ { 4 } + 8 ) =$$

Solve for D

$$\left\{\begin{matrix}D=-\frac{8\left(-x^{3}-1\right)\left(x^{4}+4\right)}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\\D\in \mathrm{R}\text{, }&x=-1\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4x^{3}+4 by 2x^{4}+8.

$$Dfx=8x^{7}+32x^{3}+8x^{4}+32$$

The equation is in standard form.

$$fxD=8x^{7}+8x^{4}+32x^{3}+32$$

Divide both sides by fx.

$$\frac{fxD}{fx}=\frac{8x^{7}+8x^{4}+32x^{3}+32}{fx}$$

Dividing by fx undoes the multiplication by fx.

$$D=\frac{8x^{7}+8x^{4}+32x^{3}+32}{fx}$$

Divide 8x^{7}+32x^{3}+8x^{4}+32 by fx.

$$D=\frac{8\left(x^{7}+x^{4}+4x^{3}+4\right)}{fx}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{8\left(-x^{3}-1\right)\left(x^{4}+4\right)}{Dx}\text{, }&x\neq 0\text{ and }D\neq 0\\f\in \mathrm{R}\text{, }&x=-1\text{ and }D=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4x^{3}+4 by 2x^{4}+8.

$$Dfx=8x^{7}+32x^{3}+8x^{4}+32$$

The equation is in standard form.

$$Dxf=8x^{7}+8x^{4}+32x^{3}+32$$

Divide both sides by Dx.

$$\frac{Dxf}{Dx}=\frac{8x^{7}+8x^{4}+32x^{3}+32}{Dx}$$

Dividing by Dx undoes the multiplication by Dx.

$$f=\frac{8x^{7}+8x^{4}+32x^{3}+32}{Dx}$$

Divide 8x^{7}+32x^{3}+8x^{4}+32 by Dx.

$$f=\frac{8\left(x^{7}+x^{4}+4x^{3}+4\right)}{Dx}$$