Factor 15x^2-4x-3

$15 x^{2} - 4 x - 3$

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 $a \cdot c = 15 \cdot - 3 = - 45$ and whose sum is $b = - 4$ .

Factor $- 4$ out of $- 4 x$ .

$15 x^{2} - 4 (x) - 3$

Rewrite $- 4$ as $5$ plus $- 9$

$15 x^{2} + (5 - 9) x - 3$

Apply the distributive property.

$15 x^{2} + 5 x - 9 x - 3$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} + 5 x) - 9 x - 3$

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

$5 x (3 x + 1) - 3 (3 x + 1)$

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

$(3 x + 1) (5 x - 3)$

Factor 15x^2-4x-3

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