Finite Math Examples

$- x^{2} + 22 x - 85$

Step 1

Factor $- 1$ out of $- x^{2} + 22 x - 85$ .

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Step 1.1

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

$- (x^{2}) + 22 x - 85$

Step 1.2

Factor $- 1$ out of $22 x$ .

$- (x^{2}) - (- 22 x) - 85$

Step 1.3

Rewrite $- 85$ as $- 1 (85)$ .

$- (x^{2}) - (- 22 x) - 1 (85)$

Step 1.4

Factor $- 1$ out of $- (x^{2}) - (- 22 x)$ .

$- (x^{2} - 22 x) - 1 (85)$

Step 1.5

Factor $- 1$ out of $- (x^{2} - 22 x) - 1 (85)$ .

$- (x^{2} - 22 x + 85)$

Step 2

Factor.

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Step 2.1

Factor $x^{2} - 22 x + 85$ 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 $85$ and whose sum is $- 22$ .

$- 17, - 5$

Step 2.1.2

Write the factored form using these integers.

$- ((x - 17) (x - 5))$

Step 2.2

Remove unnecessary parentheses.

$- (x - 17) (x - 5)$