Factor 12x^2+17x-5

$12 x^{2} + 17 x - 5$

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 $a \cdot c = 12 \cdot - 5 = - 60$ and whose sum is $b = 17$ .

Factor $17$ out of $17 x$ .

$12 x^{2} + 17 (x) - 5$

Rewrite $17$ as $- 3$ plus $20$

$12 x^{2} + (- 3 + 20) x - 5$

Apply the distributive property.

$12 x^{2} - 3 x + 20 x - 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} - 3 x) + 20 x - 5$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 1$ .

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

Factor 12x^2+17x-5

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