Precalculus Examples

$- 16 x^{2} - 16 x + 80 x + 80$

Step 1

Add $- 16 x$ and $80 x$ .

$- 16 x^{2} + 64 x + 80$

Step 2

Factor $- 16$ out of $- 16 x^{2} + 64 x + 80$ .

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Step 2.1

Factor $- 16$ out of $- 16 x^{2}$ .

$- 16 (x^{2}) + 64 x + 80$

Step 2.2

Factor $- 16$ out of $64 x$ .

$- 16 (x^{2}) - 16 (- 4 x) + 80$

Step 2.3

Factor $- 16$ out of $80$ .

$- 16 (x^{2}) - 16 (- 4 x) - 16 (- 5)$

Step 2.4

Factor $- 16$ out of $- 16 (x^{2}) - 16 (- 4 x)$ .

$- 16 (x^{2} - 4 x) - 16 (- 5)$

Step 2.5

Factor $- 16$ out of $- 16 (x^{2} - 4 x) - 16 (- 5)$ .

$- 16 (x^{2} - 4 x - 5)$

Step 3

Factor.

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Step 3.1

Factor $x^{2} - 4 x - 5$ using the AC method.

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Step 3.1.1

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 $- 5$ and whose sum is $- 4$ .

$- 5, 1$

Step 3.1.2

Write the factored form using these integers.

$- 16 ((x - 5) (x + 1))$

Step 3.2

Remove unnecessary parentheses.

$- 16 (x - 5) (x + 1)$