Factor 2x^2-5x-3

$2 x^{2} - 5 x - 3$

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 $a \cdot c = 2 \cdot - 3 = - 6$ and whose sum is $b = - 5$ .

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Factor $- 5$ out of $- 5 x$ .

$2 x^{2} - 5 (x) - 3$

Rewrite $- 5$ as $1$ plus $- 6$

$2 x^{2} + (1 - 6) x - 3$

Apply the distributive property.

$2 x^{2} + 1 x - 6 x - 3$

Multiply $x$ by $1$ .

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

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

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

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

$x (2 x + 1) - 3 (2 x + 1)$

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

$(2 x + 1) (x - 3)$

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