Basic Math Examples

$- 2 n^{2} + 11 n - 5$

Step 1

Factor $- 1$ out of $- 2 n^{2} + 11 n - 5$ .

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Step 1.1

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

$- (2 n^{2}) + 11 n - 5$

Step 1.2

Factor $- 1$ out of $11 n$ .

$- (2 n^{2}) - (- 11 n) - 5$

Step 1.3

Rewrite $- 5$ as $- 1 (5)$ .

$- (2 n^{2}) - (- 11 n) - 1 (5)$

Step 1.4

Factor $- 1$ out of $- (2 n^{2}) - (- 11 n)$ .

$- (2 n^{2} - 11 n) - 1 (5)$

Step 1.5

Factor $- 1$ out of $- (2 n^{2} - 11 n) - 1 (5)$ .

$- (2 n^{2} - 11 n + 5)$

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 $a \cdot c = 2 \cdot 5 = 10$ and whose sum is $b = - 11$ .

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Step 2.1.1.1

Factor $- 11$ out of $- 11 n$ .

$- (2 n^{2} - 11 (n) + 5)$

Step 2.1.1.2

Rewrite $- 11$ as $- 1$ plus $- 10$

$- (2 n^{2} + (- 1 - 10) n + 5)$

Step 2.1.1.3

Apply the distributive property.

$- (2 n^{2} - 1 n - 10 n + 5)$

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.

$- ((2 n^{2} - 1 n) - 10 n + 5)$

Step 2.1.2.2

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

$- (n (2 n - 1) - 5 (2 n - 1))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $2 n - 1$ .

$- ((2 n - 1) (n - 5))$

Step 2.2

Remove unnecessary parentheses.

$- (2 n - 1) (n - 5)$