Precalculus Examples

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

Step 1

Multiply $- 2$ by $4$ .

$- 8 g = 2 x^{3} - 3 x + 2$

Step 2

Divide each term in $- 8 g = 2 x^{3} - 3 x + 2$ by $- 8$ and simplify.

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Step 2.1

Divide each term in $- 8 g = 2 x^{3} - 3 x + 2$ by $- 8$ .

$\frac{- 8 g}{- 8} = \frac{2 x^{3}}{- 8} + \frac{- 3 x}{- 8} + \frac{2}{- 8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 8 g}{- 8} = \frac{2 x^{3}}{- 8} + \frac{- 3 x}{- 8} + \frac{2}{- 8}$

Step 2.2.1.2

Divide $g$ by $1$ .

$g = \frac{2 x^{3}}{- 8} + \frac{- 3 x}{- 8} + \frac{2}{- 8}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $2$ and $- 8$ .

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Step 2.3.1.1.1

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

$g = \frac{2 (x^{3})}{- 8} + \frac{- 3 x}{- 8} + \frac{2}{- 8}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $2$ out of $- 8$ .

$g = \frac{2 x^{3}}{2 \cdot - 4} + \frac{- 3 x}{- 8} + \frac{2}{- 8}$

Step 2.3.1.1.2.2

Cancel the common factor.

$g = \frac{2 x^{3}}{2 \cdot - 4} + \frac{- 3 x}{- 8} + \frac{2}{- 8}$

Step 2.3.1.1.2.3

Rewrite the expression.

$g = \frac{x^{3}}{- 4} + \frac{- 3 x}{- 8} + \frac{2}{- 8}$

Step 2.3.1.2

Move the negative in front of the fraction.

$g = - \frac{x^{3}}{4} + \frac{- 3 x}{- 8} + \frac{2}{- 8}$

Step 2.3.1.3

Dividing two negative values results in a positive value.

$g = - \frac{x^{3}}{4} + \frac{3 x}{8} + \frac{2}{- 8}$

Step 2.3.1.4

Cancel the common factor of $2$ and $- 8$ .

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Step 2.3.1.4.1

Factor $2$ out of $2$ .

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

Step 2.3.1.4.2

Cancel the common factors.

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Step 2.3.1.4.2.1

Factor $2$ out of $- 8$ .

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

Step 2.3.1.4.2.2

Cancel the common factor.

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

Step 2.3.1.4.2.3

Rewrite the expression.

$g = - \frac{x^{3}}{4} + \frac{3 x}{8} + \frac{1}{- 4}$

Step 2.3.1.5

Move the negative in front of the fraction.

$g = - \frac{x^{3}}{4} + \frac{3 x}{8} - \frac{1}{4}$

Step 3

To rewrite as a function of $x$ , write the equation so that $g$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

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