Factor 2n^2+n-6

$2 n^{2} + n - 6$

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 $a \cdot c = 2 \cdot - 6 = - 12$ and whose sum is $b = 1$ .

Multiply by $1$ .

$2 n^{2} + 1 n - 6$

Rewrite $1$ as $- 3$ plus $4$

$2 n^{2} + (- 3 + 4) n - 6$

Apply the distributive property.

$2 n^{2} - 3 n + 4 n - 6$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 n^{2} - 3 n) + 4 n - 6$

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

$n (2 n - 3) + 2 (2 n - 3)$

Factor the polynomial by factoring out the greatest common factor, $2 n - 3$ .

$(2 n - 3) (n + 2)$

Factor 2n^2+n-6

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