Factor 15x^2-29x-14

$15 x^{2} - 29 x - 14$

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 $a \cdot c = 15 \cdot - 14 = - 210$ and whose sum is $b = - 29$ .

Factor $- 29$ out of $- 29 x$ .

$15 x^{2} - 29 (x) - 14$

Rewrite $- 29$ as $6$ plus $- 35$

$15 x^{2} + (6 - 35) x - 14$

Apply the distributive property.

$15 x^{2} + 6 x - 35 x - 14$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} + 6 x) - 35 x - 14$

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

$3 x (5 x + 2) - 7 (5 x + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 2$ .

$(5 x + 2) (3 x - 7)$

Factor 15x^2-29x-14

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