Precalculus Examples

$\frac{1}{3} x^{2} + \frac{1}{3} x - \frac{2}{3}$

Step 1

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

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

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 1 \cdot - 2 = - 2$ and whose sum is $b = 1$ .

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Step 2.1.1.1

Multiply $- 1$ by $2$ .

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

Step 2.1.1.2

Multiply by $1$ .

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

Step 2.1.1.3

Rewrite $1$ as $- 1$ plus $2$

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

Step 2.1.1.4

Apply the distributive property.

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

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

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

Step 2.1.2.2

Factor out the greatest common factor (GCF) from each group.

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

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

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

Step 2.2

Remove unnecessary parentheses.

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