Factor 15x^2-19x+6

$15 x^{2} - 19 x + 6$

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 $a \cdot c = 15 \cdot 6 = 90$ and whose sum is $b = - 19$ .

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

$15 x^{2} - 19 (x) + 6$

Rewrite $- 19$ as $- 9$ plus $- 10$

$15 x^{2} + (- 9 - 10) x + 6$

Apply the distributive property.

$15 x^{2} - 9 x - 10 x + 6$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} - 9 x) - 10 x + 6$

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

$3 x (5 x - 3) - 2 (5 x - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 3$ .

$(5 x - 3) (3 x - 2)$

Factor 15x^2-19x+6

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