Factor 6n^2-11n-2

$6 n^{2} - 11 n - 2$

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 $a \cdot c = 6 \cdot - 2 = - 12$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 n$ .

$6 n^{2} - 11 (n) - 2$

Rewrite $- 11$ as $1$ plus $- 12$

$6 n^{2} + (1 - 12) n - 2$

Apply the distributive property.

$6 n^{2} + 1 n - 12 n - 2$

Multiply $n$ by $1$ .

$6 n^{2} + n - 12 n - 2$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 n^{2} + n) - 12 n - 2$

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

$n (6 n + 1) - 2 (6 n + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $6 n + 1$ .

$(6 n + 1) (n - 2)$

Factor 6n^2-11n-2

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