Pre-Algebra Examples

$- a^{2} - 7 a + 60$

Step 1

Factor $- 1$ out of $- a^{2} - 7 a + 60$ .

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Step 1.1

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

$- (a^{2}) - 7 a + 60$

Step 1.2

Factor $- 1$ out of $- 7 a$ .

$- (a^{2}) - (7 a) + 60$

Step 1.3

Rewrite $60$ as $- 1 (- 60)$ .

$- (a^{2}) - (7 a) - 1 (- 60)$

Step 1.4

Factor $- 1$ out of $- (a^{2}) - (7 a)$ .

$- (a^{2} + 7 a) - 1 (- 60)$

Step 1.5

Factor $- 1$ out of $- (a^{2} + 7 a) - 1 (- 60)$ .

$- (a^{2} + 7 a - 60)$

Step 2

Factor.

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Step 2.1

Factor $a^{2} + 7 a - 60$ 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 $- 60$ and whose sum is $7$ .

$- 5, 12$

Step 2.1.2

Write the factored form using these integers.

$- ((a - 5) (a + 12))$

Step 2.2

Remove unnecessary parentheses.

$- (a - 5) (a + 12)$