Solve for a 2x^3-2x^2-24x=ax(x+b)(x+c)

$2 x^{3} - 2 x^{2} - 24 x = a x (x + b) (x + c)$

Step 1

Rewrite the equation as $a x (x + b) (x + c) = 2 x^{3} - 2 x^{2} - 24 x$ .

$a x (x + b) (x + c) = 2 x^{3} - 2 x^{2} - 24 x$

Step 2

Divide each term in $a x (x + b) (x + c) = 2 x^{3} - 2 x^{2} - 24 x$ by $x (x + b) (x + c)$ and simplify.

Divide each term in $a x (x + b) (x + c) = 2 x^{3} - 2 x^{2} - 24 x$ by $x (x + b) (x + c)$ .

$\frac{a x (x + b) (x + c)}{x (x + b) (x + c)} = \frac{2 x^{3}}{x (x + b) (x + c)} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{a x (x + b) (x + c)}{x (x + b) (x + c)} = \frac{2 x^{3}}{x (x + b) (x + c)} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Rewrite the expression.

$\frac{(a (x + b)) (x + c)}{(x + b) (x + c)} = \frac{2 x^{3}}{x (x + b) (x + c)} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Cancel the common factor of $x + b$ .

Cancel the common factor.

$\frac{a (x + b) (x + c)}{(x + b) (x + c)} = \frac{2 x^{3}}{x (x + b) (x + c)} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Rewrite the expression.

$\frac{(a) (x + c)}{x + c} = \frac{2 x^{3}}{x (x + b) (x + c)} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Cancel the common factor of $x + c$ .

Cancel the common factor.

$\frac{a (x + c)}{x + c} = \frac{2 x^{3}}{x (x + b) (x + c)} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Divide $a$ by $1$ .

$a = \frac{2 x^{3}}{x (x + b) (x + c)} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Simplify the right side.

Simplify each term.

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

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

$a = \frac{x (2 x^{2})}{x (x + b) (x + c)} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Cancel the common factors.

Factor $x$ out of $x (x + b) (x + c)$ .

$a = \frac{x (2 x^{2})}{x ((x + b) (x + c))} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Cancel the common factor.

$a = \frac{x (2 x^{2})}{x ((x + b) (x + c))} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Rewrite the expression.

$a = \frac{2 x^{2}}{(x + b) (x + c)} + \frac{- 2 x^{2}}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

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

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

$a = \frac{2 x^{2}}{(x + b) (x + c)} + \frac{x (- 2 x)}{x (x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Cancel the common factors.

Factor $x$ out of $x (x + b) (x + c)$ .

$a = \frac{2 x^{2}}{(x + b) (x + c)} + \frac{x (- 2 x)}{x ((x + b) (x + c))} + \frac{- 24 x}{x (x + b) (x + c)}$

Cancel the common factor.

$a = \frac{2 x^{2}}{(x + b) (x + c)} + \frac{x (- 2 x)}{x ((x + b) (x + c))} + \frac{- 24 x}{x (x + b) (x + c)}$

Rewrite the expression.

$a = \frac{2 x^{2}}{(x + b) (x + c)} + \frac{- 2 x}{(x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Move the negative in front of the fraction.

$a = \frac{2 x^{2}}{(x + b) (x + c)} - \frac{(2) x}{(x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Cancel the common factor of $x$ .

Cancel the common factor.

$a = \frac{2 x^{2}}{(x + b) (x + c)} - \frac{2 x}{(x + b) (x + c)} + \frac{- 24 x}{x (x + b) (x + c)}$

Rewrite the expression.

$a = \frac{2 x^{2}}{(x + b) (x + c)} - \frac{2 x}{(x + b) (x + c)} + \frac{- 24}{(x + b) (x + c)}$

Move the negative in front of the fraction.

$a = \frac{2 x^{2}}{(x + b) (x + c)} - \frac{2 x}{(x + b) (x + c)} - \frac{24}{(x + b) (x + c)}$

Solve for a 2x^3-2x^2-24x=ax(x+b)(x+c)

Related Questions

Support LCMGCF.com by disabling your adblocker.