Factor 2x^2+19x+35

$2 x^{2} + 19 x + 35$

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 $b = 19$ .

Factor $19$ out of $19 x$ .

$2 x^{2} + 19 (x) + 35$

Rewrite $19$ 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+19x+35

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