Factor 2x^2-9x-5

$2 x^{2} - 9 x - 5$

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 $a \cdot c = 2 \cdot - 5 = - 10$ and whose sum is $b = - 9$ .

Factor $- 9$ out of $- 9 x$ .

$2 x^{2} - 9 (x) - 5$

Rewrite $- 9$ as $1$ plus $- 10$

$2 x^{2} + (1 - 10) x - 5$

Apply the distributive property.

$2 x^{2} + 1 x - 10 x - 5$

Multiply $x$ by $1$ .

$2 x^{2} + x - 10 x - 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + x) - 10 x - 5$

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

$x (2 x + 1) - 5 (2 x + 1)$

Step 3

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

$(2 x + 1) (x - 5)$

Factor 2x^2-9x-5

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