Factor 6x^2-17x+12

$6 x^{2} - 17 x + 12$

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 $a \cdot c = 6 \cdot 12 = 72$ and whose sum is $b = - 17$ .

Factor $- 17$ out of $- 17 x$ .

$6 x^{2} - 17 (x) + 12$

Rewrite $- 17$ as $- 8$ plus $- 9$

$6 x^{2} + (- 8 - 9) x + 12$

Apply the distributive property.

$6 x^{2} - 8 x - 9 x + 12$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 x^{2} - 8 x) - 9 x + 12$

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

$2 x (3 x - 4) - 3 (3 x - 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x - 4$ .

$(3 x - 4) (2 x - 3)$

Factor 6x^2-17x+12

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