Calculus Examples

$12 x^{2} - 152 x + 361$

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 $a \cdot c = 12 \cdot 361 = 4332$ and whose sum is $b = - 152$ .

Tap for more steps...

Step 1.1

Factor $- 152$ out of $- 152 x$ .

$12 x^{2} - 152 (x) + 361$

Step 1.2

Rewrite $- 152$ as $- 38$ plus $- 114$

$12 x^{2} + (- 38 - 114) x + 361$

Step 1.3

Apply the distributive property.

$12 x^{2} - 38 x - 114 x + 361$

Step 2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.1

Group the first two terms and the last two terms.

$(12 x^{2} - 38 x) - 114 x + 361$

Step 2.2

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

$2 x (6 x - 19) - 19 (6 x - 19)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $6 x - 19$ .

$(6 x - 19) (2 x - 19)$