Factor 14x^2+17x-6

$14 x^{2} + 17 x - 6$

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 $a \cdot c = 14 \cdot - 6 = - 84$ and whose sum is $b = 17$ .

Factor $17$ out of $17 x$ .

$14 x^{2} + 17 (x) - 6$

Rewrite $17$ as $- 4$ plus $21$

$14 x^{2} + (- 4 + 21) x - 6$

Apply the distributive property.

$14 x^{2} - 4 x + 21 x - 6$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 x^{2} - 4 x) + 21 x - 6$

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

$2 x (7 x - 2) + 3 (7 x - 2)$

Factor the polynomial by factoring out the greatest common factor, $7 x - 2$ .

$(7 x - 2) (2 x + 3)$

Factor 14x^2+17x-6

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