Finite Math Examples

$(x^{2} + x - 6) \cdot (x^{2} - 16)$

Step 1

The polynomial cannot be factored using the grouping method. Try a different method, or if you aren't sure, choose Factor.

The polynomial cannot be factored using the grouping method.

Step 2

Factor $x^{2} + x - 6$ using the AC method.

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Step 2.1

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 $1$ .

$- 2, 3$

Step 2.2

Write the factored form using these integers.

$(x - 2) (x + 3) \cdot (x^{2} - 16)$

Step 3

Rewrite $16$ as $4^{2}$ .

$(x - 2) (x + 3) \cdot (x^{2} - 4^{2})$

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 4$ .

$(x - 2) (x + 3) \cdot ((x + 4) (x - 4))$

Step 4.2

Remove unnecessary parentheses.

$(x - 2) (x + 3) \cdot (x + 4) (x - 4)$