Factor 15x^2-29x+12

$15 x^{2} - 29 x + 12$

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 $a \cdot c = 15 \cdot 12 = 180$ and whose sum is $b = - 29$ .

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

$15 x^{2} - 29 (x) + 12$

Rewrite $- 29$ as $- 9$ plus $- 20$

$15 x^{2} + (- 9 - 20) x + 12$

Apply the distributive property.

$15 x^{2} - 9 x - 20 x + 12$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} - 9 x) - 20 x + 12$

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

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

Step 3

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

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

Factor 15x^2-29x+12

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