Factor 2x^2-7x-9

$2 x^{2} - 7 x - 9$

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 $a \cdot c = 2 \cdot - 9 = - 18$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

$2 x^{2} - 7 (x) - 9$

Rewrite $- 7$ as $2$ plus $- 9$

$2 x^{2} + (2 - 9) x - 9$

Apply the distributive property.

$2 x^{2} + 2 x - 9 x - 9$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 2 x) - 9 x - 9$

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

$2 x (x + 1) - 9 (x + 1)$

Step 3

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

$(x + 1) (2 x - 9)$

Factor 2x^2-7x-9

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