Factor 2x^2+7x-49

$2 x^{2} + 7 x - 49$

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 $a \cdot c = 2 \cdot - 49 = - 98$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$2 x^{2} + 7 (x) - 49$

Rewrite $7$ as $- 7$ plus $14$

$2 x^{2} + (- 7 + 14) x - 49$

Apply the distributive property.

$2 x^{2} - 7 x + 14 x - 49$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 7 x) + 14 x - 49$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x - 7$ .

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

Factor 2x^2+7x-49

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