Factor 2x^2-9x-35

$2 x^{2} - 9 x - 35$

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 $a \cdot c = 2 \cdot - 35 = - 70$ and whose sum is $b = - 9$ .

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

$2 x^{2} - 9 (x) - 35$

Rewrite $- 9$ as $5$ plus $- 14$

$2 x^{2} + (5 - 14) x - 35$

Apply the distributive property.

$2 x^{2} + 5 x - 14 x - 35$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 5 x) - 14 x - 35$

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

$x (2 x + 5) - 7 (2 x + 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x + 5$ .

$(2 x + 5) (x - 7)$

Factor 2x^2-9x-35

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