Finite Math Examples

$f (x + 2) = x^{3} - 8 x - 4 f \cdot 1$

Step 1

Simplify $f (x + 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + f (x + 2) = x^{3} - 8 x - 4 f \cdot 1$

Step 1.2

Simplify by adding zeros.

$f (x + 2) = x^{3} - 8 x - 4 f \cdot 1$

Step 1.3

Apply the distributive property.

$f x + f \cdot 2 = x^{3} - 8 x - 4 f \cdot 1$

Step 1.4

Move $2$ to the left of $f$ .

$f x + 2 f = x^{3} - 8 x - 4 f \cdot 1$

Step 2

Multiply $- 4$ by $1$ .

$f x + 2 f = x^{3} - 8 x - 4 f$

Step 3

Move all terms containing $f$ to the left side of the equation.

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Step 3.1

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

$f x + 2 f + 4 f = x^{3} - 8 x$

Step 3.2

Add $2 f$ and $4 f$ .

$f x + 6 f = x^{3} - 8 x$

Step 4

Factor $f$ out of $f x + 6 f$ .

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Step 4.1

Factor $f$ out of $f x$ .

$f (x) + 6 f = x^{3} - 8 x$

Step 4.2

Factor $f$ out of $6 f$ .

$f (x) + f \cdot 6 = x^{3} - 8 x$

Step 4.3

Factor $f$ out of $f (x) + f \cdot 6$ .

$f (x + 6) = x^{3} - 8 x$

Step 5

Divide each term in $f (x + 6) = x^{3} - 8 x$ by $x + 6$ and simplify.

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Step 5.1

Divide each term in $f (x + 6) = x^{3} - 8 x$ by $x + 6$ .

$\frac{f (x + 6)}{x + 6} = \frac{x^{3}}{x + 6} + \frac{- 8 x}{x + 6}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $x + 6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{f (x + 6)}{x + 6} = \frac{x^{3}}{x + 6} + \frac{- 8 x}{x + 6}$

Step 5.2.1.2

Divide $f$ by $1$ .

$f = \frac{x^{3}}{x + 6} + \frac{- 8 x}{x + 6}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Combine the numerators over the common denominator.

$f = \frac{x^{3} - 8 x}{x + 6}$

Step 5.3.2

Factor $x$ out of $x^{3} - 8 x$ .

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Step 5.3.2.1

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

$f = \frac{x \cdot x^{2} - 8 x}{x + 6}$

Step 5.3.2.2

Factor $x$ out of $- 8 x$ .

$f = \frac{x \cdot x^{2} + x \cdot - 8}{x + 6}$

Step 5.3.2.3

Factor $x$ out of $x \cdot x^{2} + x \cdot - 8$ .

$f = \frac{x (x^{2} - 8)}{x + 6}$