Factor 7x^2-11x-6

$7 x^{2} - 11 x - 6$

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 $a \cdot c = 7 \cdot - 6 = - 42$ and whose sum is $b = - 11$ .

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

$7 x^{2} - 11 (x) - 6$

Rewrite $- 11$ as $3$ plus $- 14$

$7 x^{2} + (3 - 14) x - 6$

Apply the distributive property.

$7 x^{2} + 3 x - 14 x - 6$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} + 3 x) - 14 x - 6$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x + 3$ .

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

Factor 7x^2-11x-6

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