Pre-Algebra Examples

$\frac{1}{2} y^{2} - \frac{1}{2} y - 3$

Step 1

Factor $\frac{1}{2}$ out of each term.

$\frac{1}{2} (y^{2} - 1 y - 6)$

Step 2

Factor.

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Step 2.1

Factor $y^{2} - 1 y - 6$ using the AC method.

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Step 2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Step 2.1.2

Write the factored form using these integers.

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

Step 2.2

Remove unnecessary parentheses.

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