Factor 2x^2-3x-9

$2 x^{2} - 3 x - 9$

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 $b = - 3$ .

Factor $- 3$ out of $- 3 x$ .

$2 x^{2} - 3 (x) - 9$

Rewrite $- 3$ as $3$ plus $- 6$

$2 x^{2} + (3 - 6) x - 9$

Apply the distributive property.

$2 x^{2} + 3 x - 6 x - 9$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 3 x) - 6 x - 9$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x + 3$ .

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

Factor 2x^2-3x-9

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