Solve for c p(x)=-x^3+cx^2-4x+3

$p (x) = - x^{3} + c x^{2} - 4 x + 3$

Step 1

Rewrite the equation as $- x^{3} + c x^{2} - 4 x + 3 = p x$ .

$- x^{3} + c x^{2} - 4 x + 3 = p x$

Step 2

Move all terms not containing $c$ to the right side of the equation.

Add $x^{3}$ to both sides of the equation.

$c x^{2} - 4 x + 3 = p x + x^{3}$

Add $4 x$ to both sides of the equation.

$c x^{2} + 3 = p x + x^{3} + 4 x$

Subtract $3$ from both sides of the equation.

$c x^{2} = p x + x^{3} + 4 x - 3$

Step 3

Divide each term in $c x^{2} = p x + x^{3} + 4 x - 3$ by $x^{2}$ and simplify.

Divide each term in $c x^{2} = p x + x^{3} + 4 x - 3$ by $x^{2}$ .

$\frac{c x^{2}}{x^{2}} = \frac{p x}{x^{2}} + \frac{x^{3}}{x^{2}} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Simplify the left side.

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{c x^{2}}{x^{2}} = \frac{p x}{x^{2}} + \frac{x^{3}}{x^{2}} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Divide $c$ by $1$ .

$c = \frac{p x}{x^{2}} + \frac{x^{3}}{x^{2}} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $p x$ .

$c = \frac{x p}{x^{2}} + \frac{x^{3}}{x^{2}} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Cancel the common factors.

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

$c = \frac{x p}{x \cdot x} + \frac{x^{3}}{x^{2}} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Cancel the common factor.

$c = \frac{x p}{x \cdot x} + \frac{x^{3}}{x^{2}} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Rewrite the expression.

$c = \frac{p}{x} + \frac{x^{3}}{x^{2}} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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

$c = \frac{p}{x} + \frac{x^{2} x}{x^{2}} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Cancel the common factors.

Multiply by $1$ .

$c = \frac{p}{x} + \frac{x^{2} x}{x^{2} \cdot 1} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Cancel the common factor.

$c = \frac{p}{x} + \frac{x^{2} x}{x^{2} \cdot 1} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Rewrite the expression.

$c = \frac{p}{x} + \frac{x}{1} + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Divide $x$ by $1$ .

$c = \frac{p}{x} + x + \frac{4 x}{x^{2}} + \frac{- 3}{x^{2}}$

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $4 x$ .

$c = \frac{p}{x} + x + \frac{x \cdot 4}{x^{2}} + \frac{- 3}{x^{2}}$

Cancel the common factors.

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

$c = \frac{p}{x} + x + \frac{x \cdot 4}{x \cdot x} + \frac{- 3}{x^{2}}$

Cancel the common factor.

$c = \frac{p}{x} + x + \frac{x \cdot 4}{x \cdot x} + \frac{- 3}{x^{2}}$

Rewrite the expression.

$c = \frac{p}{x} + x + \frac{4}{x} + \frac{- 3}{x^{2}}$

Move the negative in front of the fraction.

$c = \frac{p}{x} + x + \frac{4}{x} - \frac{3}{x^{2}}$

Solve for c p(x)=-x^3+cx^2-4x+3

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