Calculus Examples

$12 x^{2} - 104 x + 169$

Step 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 $a \cdot c = 12 \cdot 169 = 2028$ and whose sum is $b = - 104$ .

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Step 1.1

Factor $- 104$ out of $- 104 x$ .

$12 x^{2} - 104 (x) + 169$

Step 1.2

Rewrite $- 104$ as $- 26$ plus $- 78$

$12 x^{2} + (- 26 - 78) x + 169$

Step 1.3

Apply the distributive property.

$12 x^{2} - 26 x - 78 x + 169$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$(12 x^{2} - 26 x) - 78 x + 169$

Step 2.2

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

$2 x (6 x - 13) - 13 (6 x - 13)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $6 x - 13$ .

$(6 x - 13) (2 x - 13)$