Solve for k p(x)=x^4-2x^3+kx-4

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

Step 1

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

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

Step 2

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

Subtract $x^{4}$ from both sides of the equation.

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

Add $2 x^{3}$ to both sides of the equation.

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

Add $4$ to both sides of the equation.

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

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Divide $k$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Divide $p$ by $1$ .

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

Cancel the common factor of $x^{4}$ and $x$ .

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

$k = p + \frac{x (- x^{3})}{x} + \frac{2 x^{3}}{x} + \frac{4}{x}$

Cancel the common factors.

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

$k = p + \frac{x (- x^{3})}{x^{1}} + \frac{2 x^{3}}{x} + \frac{4}{x}$

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $- x^{3}$ by $1$ .

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

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

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

$k = p - x^{3} + \frac{x (2 x^{2})}{x} + \frac{4}{x}$

Cancel the common factors.

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

$k = p - x^{3} + \frac{x (2 x^{2})}{x^{1}} + \frac{4}{x}$

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Solve for k p(x)=x^4-2x^3+kx-4

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