Factor 2r^2+7r-30

$2 r^{2} + 7 r - 30$

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 $b = 7$ .

Factor $7$ out of $7 r$ .

$2 r^{2} + 7 (r) - 30$

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

$2 r^{2} + (- 5 + 12) r - 30$

Apply the distributive property.

$2 r^{2} - 5 r + 12 r - 30$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 r^{2} - 5 r) + 12 r - 30$

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

$r (2 r - 5) + 6 (2 r - 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 r - 5$ .

$(2 r - 5) (r + 6)$

Factor 2r^2+7r-30

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