Factor 2b^2-9b-5

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

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 $- 9 b$ .

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

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

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

Apply the distributive property.

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

Multiply $b$ by $1$ .

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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

Factor 2b^2-9b-5

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