Factor 2a^2-5a-3

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

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

Factor $- 5$ out of $- 5 a$ .

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

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

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

Apply the distributive property.

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

Multiply $a$ by $1$ .

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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

Factor 2a^2-5a-3

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