Factor 12x^2-13x+3

$12 x^{2} - 13 x + 3$

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 $a \cdot c = 12 \cdot 3 = 36$ and whose sum is $b = - 13$ .

Factor $- 13$ out of $- 13 x$ .

$12 x^{2} - 13 (x) + 3$

Rewrite $- 13$ as $- 4$ plus $- 9$

$12 x^{2} + (- 4 - 9) x + 3$

Apply the distributive property.

$12 x^{2} - 4 x - 9 x + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} - 4 x) - 9 x + 3$

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

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

Step 3

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

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

Factor 12x^2-13x+3

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