Factor 30d^2+7d-15

$30 d^{2} + 7 d - 15$

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 $a \cdot c = 30 \cdot - 15 = - 450$ and whose sum is $b = 7$ .

Factor $7$ out of $7 d$ .

$30 d^{2} + 7 (d) - 15$

Rewrite $7$ as $- 18$ plus $25$

$30 d^{2} + (- 18 + 25) d - 15$

Apply the distributive property.

$30 d^{2} - 18 d + 25 d - 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(30 d^{2} - 18 d) + 25 d - 15$

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

$6 d (5 d - 3) + 5 (5 d - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 d - 3$ .

$(5 d - 3) (6 d + 5)$

Factor 30d^2+7d-15

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