Solve for c p(x)=x^3-4x^2+cx+33

$p (x) = x^{3} - 4 x^{2} + c x + 33$

Rewrite the equation as $x^{3} - 4 x^{2} + c x + 33 = p x$ .

$x^{3} - 4 x^{2} + c x + 33 = p x$

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

Subtract $x^{3}$ from both sides of the equation.

$- 4 x^{2} + c x + 33 = p x - x^{3}$

Add $4 x^{2}$ to both sides of the equation.

$c x + 33 = p x - x^{3} + 4 x^{2}$

Subtract $33$ from both sides of the equation.

$c x = p x - x^{3} + 4 x^{2} - 33$

Divide each term in $c x = p x - x^{3} + 4 x^{2} - 33$ by $x$ and simplify.

Divide each term in $c x = p x - x^{3} + 4 x^{2} - 33$ by $x$ .

$\frac{c x}{x} = \frac{p x}{x} + \frac{- x^{3}}{x} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{c x}{x} = \frac{p x}{x} + \frac{- x^{3}}{x} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

Divide $c$ by $1$ .

$c = \frac{p x}{x} + \frac{- x^{3}}{x} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $x$ .

Cancel the common factor.

$c = \frac{p x}{x} + \frac{- x^{3}}{x} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

Divide $p$ by $1$ .

$c = p + \frac{- x^{3}}{x} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

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

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

$c = p + \frac{x (- x^{2})}{x} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

Cancel the common factors.

Raise $x$ to the power of $1$ .

$c = p + \frac{x (- x^{2})}{x^{1}} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

Factor $x$ out of $x^{1}$ .

$c = p + \frac{x (- x^{2})}{x \cdot 1} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

Cancel the common factor.

$c = p + \frac{x (- x^{2})}{x \cdot 1} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

Rewrite the expression.

$c = p + \frac{- x^{2}}{1} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

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

$c = p - x^{2} + \frac{4 x^{2}}{x} + \frac{- 33}{x}$

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

Factor $x$ out of $4 x^{2}$ .

$c = p - x^{2} + \frac{x (4 x)}{x} + \frac{- 33}{x}$

Cancel the common factors.

Raise $x$ to the power of $1$ .

$c = p - x^{2} + \frac{x (4 x)}{x^{1}} + \frac{- 33}{x}$

Factor $x$ out of $x^{1}$ .

$c = p - x^{2} + \frac{x (4 x)}{x \cdot 1} + \frac{- 33}{x}$

Cancel the common factor.

$c = p - x^{2} + \frac{x (4 x)}{x \cdot 1} + \frac{- 33}{x}$

Rewrite the expression.

$c = p - x^{2} + \frac{4 x}{1} + \frac{- 33}{x}$

Divide $4 x$ by $1$ .

$c = p - x^{2} + 4 x + \frac{- 33}{x}$

Move the negative in front of the fraction.

$c = p - x^{2} + 4 x - \frac{33}{x}$

Solve for c p(x)=x^3-4x^2+cx+33

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