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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