Factor 14a^2+3a-2

$14 a^{2} + 3 a - 2$

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 $a \cdot c = 14 \cdot - 2 = - 28$ and whose sum is $b = 3$ .

Factor $3$ out of $3 a$ .

$14 a^{2} + 3 (a) - 2$

Rewrite $3$ as $- 4$ plus $7$

$14 a^{2} + (- 4 + 7) a - 2$

Apply the distributive property.

$14 a^{2} - 4 a + 7 a - 2$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 a^{2} - 4 a) + 7 a - 2$

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

$2 a (7 a - 2) + 1 (7 a - 2)$

Step 3

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

$(7 a - 2) (2 a + 1)$

Factor 14a^2+3a-2

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