Factor 12x^3-21x^2y-6xy^2

$12 x^{3} - 21 x^{2} y - 6 x y^{2}$

Step 1

Factor $3 x$ out of $12 x^{3} - 21 x^{2} y - 6 x y^{2}$ .

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

$3 x (4 x^{2}) - 21 x^{2} y - 6 x y^{2}$

Factor $3 x$ out of $- 21 x^{2} y$ .

$3 x (4 x^{2}) + 3 x (- 7 x y) - 6 x y^{2}$

Factor $3 x$ out of $- 6 x y^{2}$ .

$3 x (4 x^{2}) + 3 x (- 7 x y) + 3 x (- 2 y^{2})$

Factor $3 x$ out of $3 x (4 x^{2}) + 3 x (- 7 x y)$ .

$3 x (4 x^{2} - 7 x y) + 3 x (- 2 y^{2})$

Factor $3 x$ out of $3 x (4 x^{2} - 7 x y) + 3 x (- 2 y^{2})$ .

$3 x (4 x^{2} - 7 x y - 2 y^{2})$

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 $a \cdot c = 4 \cdot - 2 = - 8$ and whose sum is $b = - 7$ .

Reorder terms.

$3 x (4 x^{2} - 2 y^{2} - 7 x y)$

Reorder $- 2 y^{2}$ and $- 7 x y$ .

$3 x (4 x^{2} - 7 x y - 2 y^{2})$

Factor $- 7$ out of $- 7 x y$ .

$3 x (4 x^{2} - 7 (x y) - 2 y^{2})$

Rewrite $- 7$ as $1$ plus $- 8$

$3 x (4 x^{2} + (1 - 8) (x y) - 2 y^{2})$

Apply the distributive property.

$3 x (4 x^{2} + 1 (x y) - 8 (x y) - 2 y^{2})$

Multiply $x y$ by $1$ .

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

Remove unnecessary parentheses.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Factor the polynomial by factoring out the greatest common factor, $4 x + y$ .

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

Remove unnecessary parentheses.

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

Factor 12x^3-21x^2y-6xy^2

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