Factor 2x^2-13x+6

$2 x^{2} - 13 x + 6$

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 $a \cdot c = 2 \cdot 6 = 12$ and whose sum is $b = - 13$ .

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

$2 x^{2} - 13 (x) + 6$

Rewrite $- 13$ as $- 1$ plus $- 12$

$2 x^{2} + (- 1 - 12) x + 6$

Apply the distributive property.

$2 x^{2} - 1 x - 12 x + 6$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 1 x) - 12 x + 6$

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

$x (2 x - 1) - 6 (2 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$(2 x - 1) (x - 6)$

Factor 2x^2-13x+6

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