Finite Math Examples

$28 n^{2} - 92 n + 72$

Step 1

Factor $4$ out of $28 n^{2} - 92 n + 72$ .

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Step 1.1

Factor $4$ out of $28 n^{2}$ .

$4 (7 n^{2}) - 92 n + 72$

Step 1.2

Factor $4$ out of $- 92 n$ .

$4 (7 n^{2}) + 4 (- 23 n) + 72$

Step 1.3

Factor $4$ out of $72$ .

$4 (7 n^{2}) + 4 (- 23 n) + 4 (18)$

Step 1.4

Factor $4$ out of $4 (7 n^{2}) + 4 (- 23 n)$ .

$4 (7 n^{2} - 23 n) + 4 (18)$

Step 1.5

Factor $4$ out of $4 (7 n^{2} - 23 n) + 4 (18)$ .

$4 (7 n^{2} - 23 n + 18)$

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 $a \cdot c = 7 \cdot 18 = 126$ and whose sum is $b = - 23$ .

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Step 2.1.1.1

Factor $- 23$ out of $- 23 n$ .

$4 (7 n^{2} - 23 (n) + 18)$

Step 2.1.1.2

Rewrite $- 23$ as $- 9$ plus $- 14$

$4 (7 n^{2} + (- 9 - 14) n + 18)$

Step 2.1.1.3

Apply the distributive property.

$4 (7 n^{2} - 9 n - 14 n + 18)$

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.

$4 ((7 n^{2} - 9 n) - 14 n + 18)$

Step 2.1.2.2

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

$4 (n (7 n - 9) - 2 (7 n - 9))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $7 n - 9$ .

$4 ((7 n - 9) (n - 2))$

Step 2.2

Remove unnecessary parentheses.

$4 (7 n - 9) (n - 2)$