Basic Math Examples

$36 x^{2} - 39 x + 9$

Step 1

Factor $3$ out of $36 x^{2} - 39 x + 9$ .

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Step 1.1

Factor $3$ out of $36 x^{2}$ .

$3 (12 x^{2}) - 39 x + 9$

Step 1.2

Factor $3$ out of $- 39 x$ .

$3 (12 x^{2}) + 3 (- 13 x) + 9$

Step 1.3

Factor $3$ out of $9$ .

$3 (12 x^{2}) + 3 (- 13 x) + 3 (3)$

Step 1.4

Factor $3$ out of $3 (12 x^{2}) + 3 (- 13 x)$ .

$3 (12 x^{2} - 13 x) + 3 (3)$

Step 1.5

Factor $3$ out of $3 (12 x^{2} - 13 x) + 3 (3)$ .

$3 (12 x^{2} - 13 x + 3)$

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 $a \cdot c = 12 \cdot 3 = 36$ and whose sum is $b = - 13$ .

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Step 2.1.1.1

Factor $- 13$ out of $- 13 x$ .

$3 (12 x^{2} - 13 (x) + 3)$

Step 2.1.1.2

Rewrite $- 13$ as $- 4$ plus $- 9$

$3 (12 x^{2} + (- 4 - 9) x + 3)$

Step 2.1.1.3

Apply the distributive property.

$3 (12 x^{2} - 4 x - 9 x + 3)$

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.

$3 ((12 x^{2} - 4 x) - 9 x + 3)$

Step 2.1.2.2

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

$3 (4 x (3 x - 1) - 3 (3 x - 1))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

$3 ((3 x - 1) (4 x - 3))$

Step 2.2

Remove unnecessary parentheses.

$3 (3 x - 1) (4 x - 3)$