Factor 15x^2-7x-4

$15 x^{2} - 7 x - 4$

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 $a \cdot c = 15 \cdot - 4 = - 60$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

$15 x^{2} - 7 (x) - 4$

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

$15 x^{2} + (5 - 12) x - 4$

Apply the distributive property.

$15 x^{2} + 5 x - 12 x - 4$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} + 5 x) - 12 x - 4$

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

$5 x (3 x + 1) - 4 (3 x + 1)$

Step 3

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

$(3 x + 1) (5 x - 4)$

Factor 15x^2-7x-4

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