Trigonometry Examples

$f (x) = \frac{1}{3} x^{3} - 2 x^{2} + 3 x + 1$

Step 1

Regroup terms.

$f (x) = - 2 x^{2} + \frac{1}{3} x^{3} + 3 x + 1$

Step 2

Factor $\frac{1}{3}$ out of each term.

$f (x) = - 2 x^{2} + \frac{1}{3} \cdot (x^{3} + 9 x + 3)$

Step 3

Factor $- 1$ out of $- 2 x^{2} + \frac{1}{3} (x^{3} + 9 x + 3)$ .

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Step 3.1

Reorder $- 2 x^{2}$ and $\frac{1}{3} (x^{3} + 9 x + 3)$ .

$f (x) = \frac{1}{3} \cdot (x^{3} + 9 x + 3) - 2 x^{2}$

Step 3.2

Factor $- 1$ out of $\frac{1}{3} (x^{3} + 9 x + 3)$ .

$f (x) = - (\frac{- 1}{3} \cdot (x^{3} + 9 x + 3)) - 2 x^{2}$

Step 3.3

Factor $- 1$ out of $- 2 x^{2}$ .

$f (x) = - (\frac{- 1}{3} \cdot (x^{3} + 9 x + 3)) - (2 x^{2})$

Step 3.4

Factor $- 1$ out of $- (\frac{- 1}{3} (x^{3} + 9 x + 3)) - (2 x^{2})$ .

$f (x) = - (\frac{- 1}{3} \cdot (x^{3} + 9 x + 3) + 2 x^{2})$

Step 4

Move the negative in front of the fraction.

$f (x) = - (- \frac{1}{3} \cdot (x^{3} + 9 x + 3) + 2 x^{2})$

Step 5

Apply the distributive property.

$f (x) = - (- \frac{1}{3} x^{3} - \frac{1}{3} \cdot (9 x) - \frac{1}{3} \cdot 3 + 2 x^{2})$

Step 6

Simplify.

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Step 6.1

Combine $x^{3}$ and $\frac{1}{3}$ .

$f (x) = - (- \frac{x^{3}}{3} - \frac{1}{3} \cdot (9 x) - \frac{1}{3} \cdot 3 + 2 x^{2})$

Step 6.2

Cancel the common factor of $3$ .

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Step 6.2.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$f (x) = - (- \frac{x^{3}}{3} + \frac{- 1}{3} \cdot (9 x) - \frac{1}{3} \cdot 3 + 2 x^{2})$

Step 6.2.2

Factor $3$ out of $9 x$ .

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

Step 6.2.3

Cancel the common factor.

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

Step 6.2.4

Rewrite the expression.

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

Step 6.3

Multiply $3$ by $- 1$ .

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

Step 6.4

Cancel the common factor of $3$ .

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Step 6.4.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

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

Step 6.4.2

Cancel the common factor.

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

Step 6.4.3

Rewrite the expression.

$f (x) = - (- \frac{x^{3}}{3} - 3 x - 1 + 2 x^{2})$

Step 7

Reorder terms.

$f (x) = - (- \frac{x^{3}}{3} + 2 x^{2} - 3 x - 1)$