Factor 2x^2+5x-42

$2 x^{2} + 5 x - 42$

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 $a \cdot c = 2 \cdot - 42 = - 84$ and whose sum is $b = 5$ .

Factor $5$ out of $5 x$ .

$2 x^{2} + 5 (x) - 42$

Rewrite $5$ as $- 7$ plus $12$

$2 x^{2} + (- 7 + 12) x - 42$

Apply the distributive property.

$2 x^{2} - 7 x + 12 x - 42$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 7 x) + 12 x - 42$

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

$x (2 x - 7) + 6 (2 x - 7)$

Step 3

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

$(2 x - 7) (x + 6)$

Factor 2x^2+5x-42

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