Factor 3x^2-20x+12

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

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 $a \cdot c = 3 \cdot 12 = 36$ and whose sum is $b = - 20$ .

Factor $- 20$ out of $- 20 x$ .

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

Rewrite $- 20$ as $- 2$ plus $- 18$

$3 x^{2} + (- 2 - 18) x + 12$

Apply the distributive property.

$3 x^{2} - 2 x - 18 x + 12$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} - 2 x) - 18 x + 12$

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

$x (3 x - 2) - 6 (3 x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x - 2$ .

$(3 x - 2) (x - 6)$

Factor 3x^2-20x+12

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