Factor 2x^2+17x+30

$2 x^{2} + 17 x + 30$

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 $a \cdot c = 2 \cdot 30 = 60$ and whose sum is $b = 17$ .

Factor $17$ out of $17 x$ .

$2 x^{2} + 17 (x) + 30$

Rewrite $17$ as $5$ plus $12$

$2 x^{2} + (5 + 12) x + 30$

Apply the distributive property.

$2 x^{2} + 5 x + 12 x + 30$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 5 x) + 12 x + 30$

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

$x (2 x + 5) + 6 (2 x + 5)$

Step 3

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

$(2 x + 5) (x + 6)$

Factor 2x^2+17x+30

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