Factor 9x^2-56x+12

$9 x^{2} - 56 x + 12$

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 $a \cdot c = 9 \cdot 12 = 108$ and whose sum is $b = - 56$ .

Factor $- 56$ out of $- 56 x$ .

$9 x^{2} - 56 (x) + 12$

Rewrite $- 56$ as $- 2$ plus $- 54$

$9 x^{2} + (- 2 - 54) x + 12$

Apply the distributive property.

$9 x^{2} - 2 x - 54 x + 12$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 x^{2} - 2 x) - 54 x + 12$

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

$x (9 x - 2) - 6 (9 x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $9 x - 2$ .

$(9 x - 2) (x - 6)$

Factor 9x^2-56x+12

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