Factor 12x^2-19x+5

$12 x^{2} - 19 x + 5$

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 $a \cdot c = 12 \cdot 5 = 60$ and whose sum is $b = - 19$ .

Factor $- 19$ out of $- 19 x$ .

$12 x^{2} - 19 (x) + 5$

Rewrite $- 19$ as $- 4$ plus $- 15$

$12 x^{2} + (- 4 - 15) x + 5$

Apply the distributive property.

$12 x^{2} - 4 x - 15 x + 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} - 4 x) - 15 x + 5$

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

$4 x (3 x - 1) - 5 (3 x - 1)$

Step 3

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

$(3 x - 1) (4 x - 5)$

Factor 12x^2-19x+5

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