Factor 12x^2-24x+9

$12 x^{2} - 24 x + 9$

Step 1

Factor $3$ out of $12 x^{2} - 24 x + 9$ .

Factor $3$ out of $12 x^{2}$ .

$3 (4 x^{2}) - 24 x + 9$

Factor $3$ out of $- 24 x$ .

$3 (4 x^{2}) + 3 (- 8 x) + 9$

Factor $3$ out of $9$ .

$3 (4 x^{2}) + 3 (- 8 x) + 3 (3)$

Factor $3$ out of $3 (4 x^{2}) + 3 (- 8 x)$ .

$3 (4 x^{2} - 8 x) + 3 (3)$

Factor $3$ out of $3 (4 x^{2} - 8 x) + 3 (3)$ .

$3 (4 x^{2} - 8 x + 3)$

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 4 \cdot 3 = 12$ and whose sum is $b = - 8$ .

Factor $- 8$ out of $- 8 x$ .

$3 (4 x^{2} - 8 (x) + 3)$

Rewrite $- 8$ as $- 2$ plus $- 6$

$3 (4 x^{2} + (- 2 - 6) x + 3)$

Apply the distributive property.

$3 (4 x^{2} - 2 x - 6 x + 3)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((4 x^{2} - 2 x) - 6 x + 3)$

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

$3 (2 x (2 x - 1) - 3 (2 x - 1))$

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

$3 ((2 x - 1) (2 x - 3))$

Remove unnecessary parentheses.

$3 (2 x - 1) (2 x - 3)$

Factor 12x^2-24x+9

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