Basic Math Examples

$- 5 u^{2} - 12 u + 9$

Step 1

Factor $- 1$ out of $- 5 u^{2} - 12 u + 9$ .

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Step 1.1

Factor $- 1$ out of $- 5 u^{2}$ .

$- (5 u^{2}) - 12 u + 9$

Step 1.2

Factor $- 1$ out of $- 12 u$ .

$- (5 u^{2}) - (12 u) + 9$

Step 1.3

Rewrite $9$ as $- 1 (- 9)$ .

$- (5 u^{2}) - (12 u) - 1 (- 9)$

Step 1.4

Factor $- 1$ out of $- (5 u^{2}) - (12 u)$ .

$- (5 u^{2} + 12 u) - 1 (- 9)$

Step 1.5

Factor $- 1$ out of $- (5 u^{2} + 12 u) - 1 (- 9)$ .

$- (5 u^{2} + 12 u - 9)$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 5 \cdot - 9 = - 45$ and whose sum is $b = 12$ .

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Step 2.1.1.1

Factor $12$ out of $12 u$ .

$- (5 u^{2} + 12 (u) - 9)$

Step 2.1.1.2

Rewrite $12$ as $- 3$ plus $15$

$- (5 u^{2} + (- 3 + 15) u - 9)$

Step 2.1.1.3

Apply the distributive property.

$- (5 u^{2} - 3 u + 15 u - 9)$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$- ((5 u^{2} - 3 u) + 15 u - 9)$

Step 2.1.2.2

Factor out the greatest common factor (GCF) from each group.

$- (u (5 u - 3) + 3 (5 u - 3))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $5 u - 3$ .

$- ((5 u - 3) (u + 3))$

Step 2.2

Remove unnecessary parentheses.

$- (5 u - 3) (u + 3)$