Solve f(x)=3x^7-4x^2+15-10x^2f(x)=3x7-4x2+15-10x2

$$f ( x ) = 3 x ^ { 7 } - 4 x ^ { 2 } + 15 - 10 x ^ { 2 } f ( x ) = 3 x 7 - 4 x 2 + 15 - 10 x 2$$

Solve for f

$$\left\{\begin{matrix}f=\frac{3x^{7}-4x^{2}+14x_{2}-3x_{7}}{10x^{3}}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&x_{7}=\frac{14x_{2}}{3}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$3x^{7}-4x^{2}+15-10x^{3}f=3x_{7}-4x_{2}+15-10x_{2}$$

Combine -4x_{2} and -10x_{2} to get -14x_{2}.

$$3x^{7}-4x^{2}+15-10x^{3}f=3x_{7}-14x_{2}+15$$

Subtract 3x^{7} from both sides.

$$-4x^{2}+15-10x^{3}f=3x_{7}-14x_{2}+15-3x^{7}$$

Add 4x^{2} to both sides.

$$15-10x^{3}f=3x_{7}-14x_{2}+15-3x^{7}+4x^{2}$$

Subtract 15 from both sides.

$$-10x^{3}f=3x_{7}-14x_{2}+15-3x^{7}+4x^{2}-15$$

Subtract 15 from 15 to get 0.

$$-10x^{3}f=3x_{7}-14x_{2}-3x^{7}+4x^{2}$$

The equation is in standard form.

$$\left(-10x^{3}\right)f=3x_{7}-14x_{2}+4x^{2}-3x^{7}$$

Divide both sides by -10x^{3}.

$$\frac{\left(-10x^{3}\right)f}{-10x^{3}}=\frac{3x_{7}-14x_{2}+4x^{2}-3x^{7}}{-10x^{3}}$$

Dividing by -10x^{3} undoes the multiplication by -10x^{3}.

$$f=\frac{3x_{7}-14x_{2}+4x^{2}-3x^{7}}{-10x^{3}}$$

Divide 3x_{7}-14x_{2}-3x^{7}+4x^{2} by -10x^{3}.

$$f=-\frac{3x_{7}-14x_{2}+4x^{2}-3x^{7}}{10x^{3}}$$