Factor 30x^2-7x-15

$30 x^{2} - 7 x - 15$

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 $- 7 x$ .

$30 x^{2} - 7 (x) - 15$

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 3$ .

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

Factor 30x^2-7x-15

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