Factor 2x^2-11x-6

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

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

Factor $- 11$ out of $- 11 x$ .

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

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

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

Apply the distributive property.

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

Multiply $x$ by $1$ .

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

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

Factor 2x^2-11x-6

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