Factor 2x^2-3x-2

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

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 $a \cdot c = 2 \cdot - 2 = - 4$ and whose sum is $b = - 3$ .

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

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

Rewrite $- 3$ as $1$ plus $- 4$

$2 x^{2} + (1 - 4) x - 2$

Apply the distributive property.

$2 x^{2} + 1 x - 4 x - 2$

Multiply $x$ by $1$ .

$2 x^{2} + x - 4 x - 2$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + x) - 4 x - 2$

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

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

Step 3

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

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

Factor 2x^2-3x-2

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